There are some downsides to this looting concept. One being that finding an interesting book or audiolog that sends you on a quest somewhere will lose some context. Instead of finding it on the body of someone with environmental storytelling because you searched the place yourself it would be something your crew comes to you with and "in addition to the usual loot, we found this which is particularly interesting on a dead victim of the Spacers".

There's less incentive to thoroughly comb every nook and cranny if you can just have your crew do it. Hmmmmmmmmm. Perhaps an alternative to this is to have your companions do the search as you go along. Why not have them loot? Pick up stuff over x value. Interesting items/weapons. Have voicelines remarking on the stuff they pick up. Shout "we found something interesting over here" for important finds. Have the player and the crew loot together as part of the experience. Maybe don't allow this to happen until AFTER a player has cleared a dungeon, encouraging the player to focus on clearing first before looting because then they get the help of crew members. And you don't get that jarring experience of looting mid combat this way.

This can also allow you to keep the limitation of 1 companion for the clearance phase then having the whole crew come in to do the looting phase. Although I suspect the majority of people out there mod in the ability for multiple companions. I feel pretty strongly that 3-4 players in the player's group would make much more interesting gameplay because you can have companions talk to each other BG3 style.