I agree that dex doesn't need to be the best stat for EVERYONE but it should be the best stat for melee rogues and other finesse based martial characters. Even ignoring dexterity, It just doesn't make any sense that the only viable way to build a rogue right now in turn-based is to wear the heaviest armor possible and use slow weapons.
This is all well and good but giving you more attacks and damage baseline still doesn't resolve the issue that light armor and light weapons are strictly worse than heavier ones. I think the best solution, as was suggested, is just to remove discrete rounds and have initiative constantly determine turn order. Thus after attacking a faster character would some time get another attack before slower characters get their first. Then round based buffs/defbuffs count actions rather than rounds. This is how most tactical rpgs, like Final Fantasy Tactics and Tactics Ogre, treat it and it just makes sense, making speed have value without being overpowered. Alternatively, you could have break points like with int and debuff duration currently, or you could have something like have +10% attack speed give you +10% chance to have an extra attack. Even if dexterity, light armor, and light weapons aren't the best option, they still need to at least be an option.