I know it says in the phb that dim light means disadvantage on perception checks that rely on sight but I can't find it saying anything about how it affects combat. In practice, it means you deduct 5 from enemy's passive Perception when taking the Hide action. But strictly speaking, its only for checks that rely on sight, eg in a noisy environment.
Dim light is not cover A lightly obscured area imposes disadvantage on Wisdom (Perception) checks that rely on sight. That's the only effect it has rules as written: A given area might be lightly or heavily obscured.
Do they lose that half cover in darkness, since the rule only applied to dim light, and just have the disadvantage to attacks on them? Conclusion Dim light is not the same as cover.
In D&D 5E, dim light only affects Wisdom (Perception) checks. If I'm interpreting the Player's Handbook correctly, for combat rolls, creatures that don't have darkvision, whose target is in dim Stack Exchange Network
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.
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.
Dim light is not the same as cover. If you have an issue with the mechanics around it, think carefully about what your issue actually is before changing the rules - there may be something in the existing rules that helps, and even if there is not an ill-conceived house rule can have unintended consequences to the balance and verisimilitude of the game.