One thing to remember when considering heavier armour = damage reduction is that you create a scenario wherein you penalize those who cannot wear heavy armour, as well as fail to include other factors.
If a person in full plate was fighting an unarmoured monk, do you believe the monk would actually have a harder time hitting the person, or do you think the AC includes a representation of the damage reduction capabilities of the armour already?
If you want to add in damage reduction I don't think it's a bad idea, but I would recommend you remove the Armour Class of these items, and simply convert it from "to hit" to "damage reduction" so you're not creating the double dip scenario, wherein full plate both makes you harder to hit (which is obviously false) AND reduces damage.
I don't think you are so much punishing those who can't/won't wear armour(any) as you are providing a concrete reason for those who can to do so.
Yes, the monk would have a harder time hitting a person in plate armour to any effect- glancing blows, etc(AC).. and when they did hit, some (or all) of the blow might be absorbed.(Armor took the brunt of the hit, leaving the wearer bruised but far better off than without armour)
Personally, I think the addition of DR to armour has merit- as things stand, you can achieve near equal AC to plate armour through light armour+DEX bonus to AC, which comes with all the inherent benefits of DEX for free- higher initiative, acrobatics, stealth etc, and none of the detriments (disadvantage on stealth, time to don/doff, potential movement speed penalties).