This is one area where I feel strongly that D&D should resemble reality, in that wearing armor in combat is always preferable to not wearing armor in combat. The only people who should ever willingly go into combat without armor are people who cannot wear armor at all, or people who need to go without armor when they're not in combat.
And, quite frankly, the solution to this problem is as realistic as it is simple: stop penalizing characters' Armor Class for wearing armor. This is an artifact brought over from Rolemaster, in which the penalty to DB was more than offset by the protective benefits of the armor; it has absolutely no place in a game like D&D which makes no distinction between 'hit' and 'hurt'. In a game like D&D, it is neither balanced nor realistic.
Even if you have a Dexterity of 20, your Armor Class should be better in heavy armor than it is in light armor. Thus, if you absolutely must penalize Dexterity for wearing heavy armor, the amount of penalty-- for any near-human level of Dexterity-- must be smaller than the amount of difference between the AC granted by the best 'normal' light armor and the worst 'normal' heavy armor.
Let's go with 20 Dexterity, since that's our assumed PC maximum. That's +5 to AC. Now, assuming-- for the sake of argument-- that a man in heavy armor shouldn't be able to get any benefit from his Dexterity... that means that a full suit of chainmail needs to be at least five points better than a simple chain shirt. That doesn't make sense to me, I don't think it makes sense to anyone else, and it makes chainmail too damned good for people with no Dexterity bonus.
On the other hand, if Light Armor is no penalty, and Heavy Armor restricts the bonus to half your Dexterity bonus... then the minimum difference only has to be 2 points. Which makes a little more sense, with a chain shirt being only half of a full suit of chainmail and probably being made of lighter chain.
Then, the only way to have a better Armor Class fighting in light armor versus the equivalent heavy armor is to have superhuman Dexterity-- at least 22-- in which case, it actually might, possibly, make a little sense.