There are a lot of good responses here, and a lot of things worth considering.
I do think "armor as DR" can work as a system, when that system is built for it from the ground up. DnD wasn't built for it, and I feel that leads to some bizarre things. Sure, DR helps you reduce low-damage attacks, but even by level 5 you have enemies like Hill Giants that hit HARD, but have slightly less accurate attacks. A fighter now would just get smashed by anything like that, because they cannot dodge and the DR isn't as effective against the high average damage.
I also agree that making Dex even more important for all builds is... rough.
Like the idea of, if you implement this, increasing the bonus from shields.
You just need a soft cap on reduction. So even if your DR could reduce it to 0 it deals X damage.
Pulling this out, I actually find this kind of a problem, and he did suggest a soft cap of 1. And maybe this gets to the different philosophies between me and the designer.
Previously, if a level 2 Paladin had chain, a shield, defensive style, and Shield of Faith, they could get an AC of 21. If they were then facing a squad of goblin archers, let's say four of them, then even if the goblins are hiding and firing from cover, they are very unlikely to hurt the paladin. They may get a lucky shot, but most of these blows just bounce off.
Now, this can be frustrating. As the DM, I hate missing and feeling like my monsters are powerless as much as I dislike it as a player. It is human nature, but the moment is awesome for the party.
Under this new system, the Paladin may only have an AC of 12, with a DR of 9. Now, especially with advantage, the Paladin is in deep trouble. Those goblins aren't going to miss, they are going to consistently hit that 12. If they have advantage, that reduces his DR to 4. So, he's taking 1 or 2 damage from every single shot.
Where before, the goblins were fleeing, because they could not hurt this terrible juggernaut, now the paladin will be forced to flee because they can't survive this onslaught for long.
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I do like the idea of including DR into armor. Heavy Armor Master is a fun feat and I like the idea of expanding on it, maybe making it a function of special armors, but I think adding DR without lowering AC is pure buffing to some strong classes, while lowering AC feels bad to me.