Bulletproof armor does exist in the Timely system, but it's not truly bulletproof in the sense that it's limited use.
Given that at least three of the Defenders can tank bullets without it, it's the sort of thing that's not terribly useful unless you can afford to keep replacing them. But fortunately for Fury, government pockets run deep.
Honestly it wouldn't surprise me if that's why Hawkeye does it in the MCU. Everyone expects S.H.I.E.L.D. agents to come in either throwing hands or firing guns, no one expects someone rocking up with a bow and arrow. XD
To be 100% fair to Loki, he doesn't have access to Fury's character sheet.
But on the other hand, absolutely correct, neither Loki's Intelligence nor Wisdom scores are especially high. Int's a bit higher of the two, but still.
Author Notes:
Given that at least three of the Defenders can tank bullets without it, it's the sort of thing that's not terribly useful unless you can afford to keep replacing them. But fortunately for Fury, government pockets run deep.