It's not cover and will be awkward to interpret with a similar mechanical implementation
The official mechanics treat cover as a physical barrier to attacks-- a target behind cover has a smaller "hit box" than normal because the attack could hit the barrier instead of landing a meaningful blow on the target. This is represented with extra AC.
The tradeoff for that extra AC is (usually, in my experience at least) about tactical positioning: it's rare for a creature to enjoy cover and also be mobile. Exceptions of course exist, such as a fortified position designed to offer cover and mobility in a useful range.
I definitely understand the temptation to treat unfavorable lighting conditions similarly: a harder-to-see target is also harder to hit because it's harder to aim at them effectively. But in practice I have not been pleased with the results, which have primarily been that combats take longer without being more fun or interesting. When enemies have the extra AC and decent freedom of movement the situation is almost the same as just giving them a higher AC and not fiddling with the battlefield or enemy tactics at all. And a higher AC can matter a lot in how a fight plays out.
Poor lighting fits better with hiding and perception mechanics in 5e than it does cover mechanics.
The reasons I believe this to be the case are:
- There is no generic mechanic for precise aim (certain class
features from Tasha's Cauldron of Everything not withstanding).
The most specific target you can aim for, RAW, is a 5-foot cube. There are no called shots.
- Because the most precisely defined target you can try to hit is a
square on the grid, knowing which square a target is in provides the
maximum chance-to-hit scenario possible.
- When you don't know which square a target is in, there already exist
mechanics for guessing their location on an attack roll in the
Unseen Attackers and Targets section of the PHB (Chapter 9, Making an Attack, Unseen Attackers and Targets).
If you rule that it's harder to hit a target in poor lighting, applying Disadvantage represents that difficulty in a more streamlined way than designing a whole new suite of mechanics. This is exactly the kind of situation that Disadvantage was intended to address, and it's not more of a modification to overrule the bullet points noted in the question than it is to homebrew a bunch of new systems and rules.
The way that combat in D&D 5e shakes out, AC is frequently not that important a feature for determining tactics. The usual decision is between using Actions for things with attack rolls versus using Actions that force saving throws, though of course the DM can vary things.
In that light (pun not quite intended), I'll ask this regarding using poor lighting as cover: what tactical possibilities do you believe arbitrarily raising AC will open up, and do you have plans for other mechanical applications of lighting conditions beyond just raising AC?
The more thorough and well-planned yes answers you have to those questions, the more reasonable adding a homebrew mechanic around poor lighting adding AC seems to me. I'm not necessarily endorsing that approach, but examining those questions is how I would approach the possibility.
Lighting conditions and Disadvantage
Manipulating light is not very hard to do in most cases in 5e: the Darkness spell trivially gives every advantage darkness offers, and a variety of easily available items (like torches) and common spells that don't drain limited resources (like Light) fix various types of darkness. This could offer new tactical possibilities, like having a player dedicated to battlefield control by cleverly moving lights around, even with the RAW lighting rules. If the benefits of battlefield light management are too strong, however, then many players will essentially never not use them. And you'll have to balance combats for the extra advantages of those tactics, so players will effectively penalized for not managing light.
Advantage and Disadvantage are significant enough that they are worth getting/avoiding when convenient, but are not always worth a huge resource expenditure to obtain: spending a turn solely to gain Advantage on the next turn's attack is generally worse than just attacking once on each turn. Bonus AC is a different story, and is often much more valuable than Advantage/Disadvantage. One PC, trivially and reliably offering AC bonuses of +2, +5, and +∞ to the party while denying those to opponents, seems to me to be too strong an incentive. Advantage and Disadvantage, as more modest benefits, can be situationally great choices but not so amazing that players must employ strategies to get them at every possible opportunity.
How I would respond to your proposed lighting systems as a player
Light management would boil down to two situations for me: ambient bright light, and ambient darkness.
In ambient bright light, I would cast (or otherwise establish) Darkness and maintain it at all times, enveloping my party. This would give us easily moveable cover, granting an extra 2, 5 or infinite AC (depending on how much cover you rule it would offer). Additional castings of Darkness, with other characters, makes the approach even better.
If you tried to limit the cover bonus to dim lighting only, I would probably complain-- why would dim lighting provide more of the benefit than total darkness? This situation could get pretty close to a "never lose" setup. There would be very few situations in which light management is possible but this particular tactic is not. This might be a strongly dominant strategy (though I haven't run the numbers on it), meaning that doing otherwise is always a worse choice. That is the opposite of tactical variety.
In ambient darkness, I would employ creatures with low combat value (familiars, charmed beasts, hirelings, etc.) to move around with torches, items under effects of the Light spell, and similar. Using preplanned tactics, shouted utterances, and Readied Actions/Movement I would work to ensure that enemies are always in bright light and that the PCs never are. If there is an AC bonus to being in dim light, that only makes the tactics more flexible because less movement is required to gain or remove lighting-derived AC bonuses.
Cover bonuses for poor lighting seem to me to be so good that you won't see PCs ignoring these applications any more often than you see a low INT Wizard or low CON Barbarian. Conversely, Advantage and Disadvantage would be more likely to provide emergently beneficial situations (given where we are and what the battlefield is like, can I maneuver the enemy such that I'm in dim light while they're in bright light?), but are not so good that I would make a point of using spell slots and turns to set them up for myself and my whole party. It may still be a good tactic, but is not so dominant.
What I've done with light and darkness
In combats I use darkness almost exclusively for a couple of purposes: to restrict movement (a PC doesn't know what they might run into, and so may be more cautious) and/or to give enemies an edge in tactical positioning. I like the idea of more effects, but lighting is not a very rich mechanic in 5e and so I have found those to be best when limited to gimmicks in individual fights rather than new rule systems.
PCs with less effective room to maneuver tend to view the battle differently than if moving were easier. Enemies in the darkness can use the Hide action more effectively than would otherwise be possible, and if hidden they get Advantage on attack rolls. In my experience, those situations cause players to think up and use different tactics than they favor in well-lit situations.
True, those tactics often involve fixing the lighting through various means, but using one or more turns to do that can still be an interesting choice. Characters with Darkvision are supposed to be extra-effective in poor lighting, and nerfing that because you think lighting can be a more interesting mechanic is often viewed as poor form for a DM. There are opportunity costs to having Darkvision, and so the benefit should exist if a player chooses that trait. It would be similarly inappropriate to arbitrarily inhibit an elf's resistance to being charmed or immunity to being magically put to sleep just because you want to deploy tactics based on those effects.
Example in practice: I had four PCs in a pitch-dark crevasse with limited floor space. The first things they did were to throw down a torch and items with Light cast on them, creating two bubbles of light they didn't dare step out of. Meanwhile, a group of Slithering Trackers snuck around outside of those bubbles, hiding effectively, and were able to strike from unexpected angles and at unexpected times. They ultimately split the party between the two light bubbles and nearly achieved a TPK.
It ended up being an exciting, harrowing, and memorable experience for the players because of the mood of the situation itself. The fight would have been very different if it had been focused around knowing where the enemies were more of the time but having more trouble hitting them. The extra turns even a marginal increase in AC would have granted would almost certainly have led to a TPK (though, had I used higher average AC per round, I would have prepared the combat differently). Even if a PC had had Darkvision, that wouldn't have helped the other players very much, especially after I succeeded in splitting the party.