So your ability to hit monsters doesn't change, without magic items; it even falls behind if you pick up feats instead of ability boosts. But the ability for monsters to hit you continues to grow, unless you use magic items to boost your AC.
Now, this might be because there are more ways to boost your AC than there are ways to boost your attack. It's still weird, and I'm not sure that I like it.
It's classic feel all the way, that's exactly what the game's been like for most of its history. You have more hps (tons more in 5e), and, in AD&D you had across-the-board scaling Saving Throws to help you survive being hit more.
I guess a corner case where it kinda breaks down a little is if you have a hypothetical series of monsters over a range of levels that forced a save on a hit, and were hammering your 'bad' (non-proficient, tertiary-stat) save. They'd not only hit you more often for more damage, but the save would get harder and harder for you to make - you'd be getting 'worse' as you leveled.
In order to put in scaling player AC, though, we'd either need to base AC at 8 + modifiers, like save DCs, or we'd need to bring back weapon proficiency bonuses, which would seem odd in the system when they already have proficiency bonuses.
Adding in proficiency to AC would require a lot of changes.
Or just not have it stack with armor. The 5e general rule is already that different AC formulas don't stack. So you have 'active defense' or 'parry' or whatever:
8 + Proficiency Bonus + DEX
All other AC formulas stay the same. It acts as a 'floor' for armored characters who lose their armor or are forced to use sub-standard-for-their-level armor.
If you want to make it interesting, let any stat stand in (perhaps only under a given condition) for DEX.
For instance a wizard could have a defensive proficiency:
Magic Wards: AC = 8 + Prof + INT when conscious, able to speak, has a hand free, and is not Concentrating.
Melee types might have 'parrying:' AC = 8 + Prof + STR (if using a regular weapon), DEX if using a light weapon, or CON if using a Shield.
Etc...