I'd love to see armor as damage reduction. But doing so is becomes a game balance and complexity issue. How complex do you want to make combat? You'll still need to adjudicate how hard it is to hit a creature. Is that now based on comparing martial skill, circumstances, corresponding attack/defense modes and battlefield conditions? Do varying armors provide sliding DR for varying damage types? Does it degrade with repeated damage?
The thing that appeals to me most about 5e is it's design simplicity and elegance. You can accomplish a lot of varied activities in a satisfying manner with it and it flows quickly. It's not something I want to sacrifice for more 'realism', though it something I'd love to see implemented some day.
That's why I use resistance and immunity in my "armor as DR" approach, to maintain consistency and simplicity.
In most cases there are options to overcome the resistance. For example, chainmail and plate are immune to attacks by slashing weapons (such as a sword), but most swords can also be used as thrusting (piercing) weapons. This armors are also resistant to piercing weapons, but there are specialized weapons (such as an estoc) that is designed specifically to pierce armor. Bodkin arrowheads also overcome the resistance, as do some fighting styles.
Really, all that you need to know when attacking, is if you have an ability that overcomes whatever resistance the target might have due to armor.
I have a separate equipment damage system if you want to track that. It doesn't come into play often, because we assume that when the party camps at night part of what they are doing is maintaining their equipment.
Here's the basics:
Textile Armor: Resistant to ranged piercing weapons that are not magical
Composite Armor: Resistant to ranged piercing weapons, and slashing weapons that are not magical (a chain shirt and scale mail have the same resistances)
Mail Armor: Resistant to piercing weapons, and immune to slashing weapons that are not magical
Plate Armor: Restistant to bludgeoning and piercing weapons, immune to slashing weapons that are not magical.
Some people question this, and ask why doesn't everybody wear the "best" armor? My answer is "they do."
They always wear the best armor they can afford that doesn't interfere with whatever else they are doing. That just makes sense to me. But those wearing heavier armor have a greater chance of fatigue in my campaign, in regions where that type of armor is common, it's also fairly common that tactics and weapons have been developed to overcome the armor, and in the end it doesn't seem to change things all that much.
But at lower levels, or for low level NPCs (town guard, for example), it makes a very big difference. I'm still tweaking the exact AC that armor provides under this system. For example, somebody with a high Dexterity might be harder to hit (higher AC), but takes more damage if they are hit. That's sort of the trade-off that I think armor provides, but only if you're well trained.