My players are very happy with 5e, but they are not pleased with the armor system. If you get hit, it doesn't matter at all whether you wear armor or not.
I was thinking of a house rule where heavy armor was fairly easy to hit (because the weight and reduced vision), but it soaks damage. Say AC 14-15.
Light armor would be harder to hit (the defender can feint, dodge, and maneuver) but it soaks very little. Say AC 20-22.
I'm still pondering shields. Historically, a medium shield was both a parrying device and a weapon.
Well, as you say, "If you get hit, it doesn't matter at all whether you wear armor or not."
Except,
getting hit is where the armor helps you. But armor and AC aren't about getting hit, they are about avoiding damage. In D&D better protection (i.e. higher AC) means less damage, which is basically their version of the soak. It is pretty abstract, really, and I explain to new players that simply because you failed to beat the AC, there was still a good chance you "hit" and made physical contact.
Heavy armor, despite the weight, was well-balanced and still allowed a great level of maneuverability. You could move, duck, dodge, feint, etc. just about as well as you could in light armor. The only reasons people wore lighter armors was because they were cheaper and easier to manufacture.
Light armor does allow someone to use all their DEX, so in that sense they are harder to hit and damage.
Your idea of getting light armor up to AC 20+ is pretty high IMO. If you insist on doing it, I would suggest the following system:
Unarmored or Light Armor: You add double your DEX modifier to your AC. DR 1 point.
Medium Armor: You can add up to your full DEX modifier to your AC. DR 2 points.
Heavy Armor: You can add up to half (round down) your DEX modifier to AC. DR 4 points.
This will raise ACs quite a bit, but that might be more to your liking. Light armors (AC 12 max) with DEX 20, would give AC 22 max. Medium armor (AC 15) with DEX 20 would be AC 20 max. Heavy armor (AC 18) with DEX 20 would also be AC 20 max. The stronger armors offer more DR, so are still worth having.
Another option if you don't want higher ACs in general is this:
All armor values (AC - 10) are divided in half. The larger portion (if unequal) is AC, the smaller portion is DR. Some examples:
Studded Leather (AC 12) becomes AC 11 with 1 DR.
Breastplate (AC 14) becomes AC 12 with 2 DR.
Splint (AC 17) becomes AC 14 and 3 DR.
Normal DEX rules apply (full for Light, +2 max for Medium, none for Heavy).
With max DEX 20, Light armor can give you an AC 16, two points better than Plate or Splint (AC 14). The best medium would give is Half-Plate (AC 13) with +2 DEX would be AC 15. So, Light can be better than both as far as AC is concerned.
This system works well if you want to keep ACs more typical for 5E but desire armor to provide some level of soak or DR.
All shields, not just medium, were used offensively when the chance presented itself.
For shields, we have four variants at our table:
Buckler (AC +1), 1d4 bashing damage if used as an improvised weapon, has the Light property
Normal (AC +2), 1d4 bashing damage
Heavy Shields (requires separate proficiency, STR 13, only Fighters start with it, disadvantage on Stealth):
Kite (AC +3), 1d6 bashing damage
Tower (AC +4), 1d6 basing damage
Characters without STR 13 can use them still, but only gain AC +2.
Anyway, hope some of those ideas help you. Good luck.