Background

In the Player's Handbook, it is specified that Advantage and Disadvange sources effectively "cancel out" regardless of how many there are of each:

If circumstances cause a roll to have both advantage and disadvantage, you are considered to have neither of them, and you roll one d20. This is true even if multiple circumstances impose disadvantage and only one grants advantage or vice versa. In such a situation, you have neither advantage nor disadvantage.

Intuitively, this rule makes sense, but it results in some very bizarre consequences mechanically, especially where multiple Disadvantage sources (which is far more common than having multiple Advantage sources) are concerned.

Take, for example, creature A firing a Longbow from 550' away at their (aware and engaged in combat) target, creature B:

• From being 550' away, creature A has a source of Disadvantage


• 
  THEREFORE, creature A has disadvantage on their Attack Roll

Now consider the scenario where this same creature A first steps into an area of thick Fog before attempting their shot, and is therefore no longer able to see their target (and vice-versa; creature B can no longer see creature A). They're still aware of creature B's location (because creature B has not yet moved), but nonetheless they cannot see them.

• From being 550' away, creature A has a source of Disadvantage


• From (creature A) being unable to see their target, creature A has a source of Disadvantage


• From (creature B) being unable to see their attacker, creature A has a source of Advantage
  


• 
  THEREFORE, creature A has neither Advantage nor Disadvantage on their Attack Roll (???)

Do you see the problem? By doing something that, by all objective logic, should have made that shot more difficult by obscuring vision to their target, they have instead made their shot easier; blinding themselves caused a significant boost to their shot accuracy.

My Proposal

To fix this issue, I'm proposing allowing Multiple Disadvantage sources to still take precedence over a lesser number of Advantage sources. This rule would not be symmetrical; it would not be possible to gain Advantage while having any number of Disadvantage sources. This is my proposed [re-]wording of that paragraph:

Variant-Multiple sources of Advantage or Disadvantage. If circumstances cause a roll to have both advantage and disadvantage, tally up the sources of Advantage and Disadvantage conferred upon that roll. If the number of Disadvantage sources exceeds the number of Advantage sources, the roll has Disadvantage. Otherwise, the roll is made without Advantage or Disadvantage; having an excess of Advantage sources will not result in a roll that has Advantage.

The intent of this rule is to make it less feasible for characters to make weird "trick shots" like what I've outlined above, where a course of action that should logically make an action more difficult instead makes it easier.

Are there common/notable situations where this ruling could backfire instead? If so, what are those circumstances?

Why not Symmetrical?

The short version is that Advantage, to me, represents circumstances where a character is especially able to perform whatever task they are trying to perform, be it dodging the blast of a Fireball, or successfully making a shot with an Arrow. If there are circumstances that are interfering with their ability to do so, even if they are receiving a lot of bonuses to their capabilities, those interferences should generally negate whatever ease they were otherwise experiencing.

It complicates what is intentionally simple.

One of the aims of the advantage/disadvantage system is to remove the payoff for "bonus-scrounging". It isn't desirable to have your players constantly trying to find one more reason to get a little plus in their column; that has historically led to a lot of friction, book-diving, and absurd arguments to realism ("I'm standing on the table so I have a high ground bonus against him!"). By making only one advantage 'count', your players are more likely to focus their attention on finding one strong narrative (or mechanical) reason they should have advantage, and then stop looking and roll the dice already.

Your proposed rule partially brings us back to that place -- when there are X disadvantages in play, the players are suddenly strongly incentivized to try to find at least X advantages to balance it back out. Instead of looking for one decent source of advantage, they're hunting for enough to balance things out, and you're back to jumping on tables.

But you may be trying to fix the wrong problem.

From your question, I'm not sure whether you actually have a problem with the advantage system as a whole, or if you're really just seeing a problem with a specific sort of scenario and aiming a little too broadly with your fix.

Your example scenario with the fog cloud does highlight an issue I've noticed myself -- I personally think the "unseen attacker" rules are a little hinky. But the problem is in the "unseen attacker" rules, not in the advantage system itself.

It would be easier and less intrusive to make a houserule that modifies the "unseen attacker" rule to say something along the lines of "When you can see a creature but it can't see you, you have advantage on attack rolls against it." Then going from a disadvantageous shot to a double-blind scenario doesn't improve your odds; if you're both blinded to each other, such as by a fog cloud, you both attack at disadvantage, which makes sense both narratively and logically.

That fix would solve the issue you've identified but wouldn't require making the overall system more complicated -- if that's the only thing bothering you.

It's overkill

I'm going to challenge your premise and recommend that instead of attempting a system overhaul to handle edge case exploits, you simply rule at your table when something is attempting an exploit that it won't work.

This avoids having to rebuild a system that generally works and allows you to handle the edge cases simply. I don't think players will raise much fuss when it's explained as long as you keep it fair and reasonable - but you do still need to watch out for when it is reasonable and within the rules.

Otherwise, looking at counting the instances and tracking them may work better for you and your table and avoids the need to completely redesign the system in an asymmetrical way (although stacking carries it's own concerns.)

It may lead to more unfun events

By making this asymettrical, you may be inherently raising the number of disadvantage instances. If that's the case, then you are making it more likely a PC is going to be rolling at disadvantage when they RAW wouldn't - and that may lead to unhappy players.

You've misinterpreted the sample situation

The following part of your question is the key to your complaint, but only because you've interpreted it with a phrasing that lacks verisimilitude (the bold emphasis was yours, but it's also what I'm emphasizing):

By doing something that, by all objective logic, should have made that shot more difficult by obscuring vision to their target, they have instead made their shot easier; blinding themselves caused a significant boost to their shot accuracy.

Nope. Since multiple disadvantages don't stack, the attacker blinding themselves by stepping into the fog cloud didn't cause a boost to their shot accuracy; it had literally no effect because the target was already unreasonably far away. Rather, causing their target to be unable to see them did grant an advantage that caused a significant boost to their shot accuracy by tipping the scale back in the attacker's favor.

The only difference in the calculus is the advantage gained by making the target unable to see the attacker, and that's exactly what the attacker should have had in mind anyway by leveraging the fog cloud: the attack was already a literal long shot, but it was made a little more tenable by rendering the target unable to see it coming.

Your scenario as you presented it is only an issue of phrasing. When phrased with verisimilitude, no such issue occurs and the system works as intended.

If it isn't broke, don't fix it

It doesn't appear to me that there's an actual problem to fix, so it seems problematic to consider overhauling what is designed to be a simple system to handle an edge case that only exists as a matter of phrasing.

However, if you're going to fix what you perceive to be a problem, don't throw the baby out with the bathwater. The system as it is works fine most of the time. If it ever doesn't, then you as the DM have the power and the mandate to say that it doesn't. If you think the fog cloud should not benefit the attacker in this scenario, then just make that ruling. That's a lot simpler for you and for the players than requiring everybody to remember a new rule.

It overpowers disadvantage stacking, and underpowers other spells/abilities

While your proposed system addresses the realism factor to a degree, mechanically it changes the game in a way that can be frustrating, as it completely negates the balancing effect certain spells and abilities have on advantage/disadvantage.

For example, suppose your Enemy has Blur and Foresight up and is able to poison you. Even if your ally manages to restrain them and someone uses the Help action, you're still going to be at disadvantage, rendering mechanics that negate disadvantage like help/flanking useless unless you can stack enough of them to even hit neutral. Stacking multiple effects becomes an arms race between stacking disadvantage to guarantee it, or to gaining enough stacked advantage to simply negate it.

The choice to keep it limited to cancellation is easier for tracking, prevents overpowered stacking, and keeps things running smoother overall. It's not perfect, but for the majority of cases it does well at approximating in a way that is simple and fun. As with many edge cases, specific DM ruling in a situation can often be better than broad rule changes.

My main concern would be that by allowing this, you are bringing back the bean counting problem that 5ed was trying to avoid. 5ed is streamlined so that combat can be fun and (relative to earlier editions) quick. So I would only allow this in the cases in which bean counting is fun for your group, and I would keep it symmetrical so that spells/abilities that grant you advantage aren't under-powered to disadvantaging your opponent. (No one likes their abilities being situationally nerfed against them)

I would also like to point out that the simulation you proposed hasn't actually broken down as you claim. Creature A is beyond the accuracy range of his weapon. He has disadvantage because No amount of skill/help can guarantee the arrow will hit any particular location. Blinding himself does not really add disadvantage because the shot is already a kind of Hail-Mary shot. However, by obscuring his shot, the person being shot at can no longer see when a projectile is fired, so they need to notice a very small, very fast moving object leave a fairly large area, before it possibly hits them in the face. Both parties have to deal with long shot odds, so it mostly balances out.

This is why 5ed opts for canceling. Disadvantage on disadvantage doesn't really stack, but reinforce the situation as sub-optimal, same with advantage. 2 types of disadvantage do not automatically create super-disadvantage. So realistically, after advantage AND disadvantage have been established, it's already anyone's game and nothing will really meaningfully change the odds from there.