You'll want to think about how to handle monks and barbarians, who get a max AC of up to 26 in this system.
This is probably the biggest concern. Without those classes, it would probably balance out with magic armor at higher levels.
Armor is a fairly universal concept, though. It's just the nature that changes. The only reason armor feels "impractical" in a modern setting is because the setting is less abstract to us. It's not like the average yeoman, or even bandit, actually wore even light armor in the Middle Ages. Modern cops, soldiers, and high-end security guards all wear armor.
Those are more equivalent to the PCs.
If you're running a modern setting, reskin leather to a biker jacket, studded to basic Kevlar vest (wearable under shirt), chain shirt to heavy Kevlar vest/jacket, breast plate to Kevlar with metal/ceramic inserts, chain mail to standard riot gear, and full plate to heavy combat armor.
If you're going to go the other direction (cave man/barbarian), then it's a matter of just how many skins the PC wants to pile on. Max armor probably is medium. Roman or Greek era would be appropriately limited, with a max at around medium. Both settings would be countered by having lighter weapons (no longsword or longbow). If you went with more monstrous opponents, you're starting to break out of strictly historical stuff, so feel free to let them have easier access to magic armor, rather than heavy armor.
Ultimately, though, 5E armor rules tend to balance out between heavy fighters with high strength and light fighters with high dexterity. Any setting that favors low/no armor is probably going to also favor easily concealed (and generally more finesse) weapons, anyway. If you do end up with a strength-based Heracles, just let him have a Nemean Lion skin to wear.
