This run was inspired by a comment, and since I liked the idea so much, I just had to do it! In this run, I can only use gear obtained from piles, lockers, and small chests. No large and red chests, no toilets, no loot from enemies, and no vending machines. I allowed myself to loot ammo from containers, mostly because I would do it out of habit either way.
This run was painful. The early game was almost normal, but from the Bloodshot Stronghold on, I was always using under-leveled gear, which is possible for some areas, but very slow and difficult.
If you're wondering where the TTWL run is, I'm working on it. A combination of getting addicted to other games and not knowing what character I wanted to create delayed it by a bit.
Also, my Discord server, since people like that: https://discord.gg/Eq3VrncPBK.