What incentive (if any) would the guy in plate armor have for wearing it?
Very true, but think about it: you buy armor to protect you, but then when you are hero of the realm you don't need it anymore and put on a suit of studded leather. AC is the same, but now your skill is so good you doesn't need the heavy armor (despite wearing it for dozens of adventures and it saving your life over and over again). There's no incentive to continue wearing the armor that you've been using.Pick one: because you would be denied your PB when you would be denied your Dex bonus, or it fits the image (cf. Hollywood Heroics).
Note that at low levels Plate is strictly better, giving a base AC of 18 rather than 12+3 = 15.
I would consider something like this:
The +1 per tier is simple of course, but doesn't help light and medium armor wearers like the OP was trying to do.I think that fails the KISS principle.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.