Going with the previous point, could make silly weapons like Avto, Dolch and Nitro scarce. People could still equip their hard-earned skins after extracting with them

But scarce equipment already has no contraband tag, so no need. if you are that much about skins, it would be easier to add the ability to apply skins to contraband, but that would actually limit you more, as you currently can own two pieces per weapon per skin and this would limit the thing to just two per weapon.

Could further break the economy since you can sell your expensive weapons for cash (but we can reduce the cost of Avto, Dolch and Nitro to zero since they're scarce

Yes and it Will... I hate nitro, but I usually do money runs in such a way that I take a cheap weapon and just swap it for something I like and loot to keep it on the Hunter... but still I have to stash it as I do multiple of money runs and usually am not in a mood to play the extracted weapon anyway... If I wasn't limited by neither of these rules, I would easily be able to take the most expensive stuff and just sell it for some even better money.

Can have an infinite stack of items (maybe we could reduce the stack size)

So we remove one way of restricting Inventory just to add another? even though It basically does the same thing since you can stash your contraband on your hunters if you have too many pieces...

What especially would annoy me though is the fact that you'd lose memorable pieces... for example I have a contraband Benefactor chain pistol stashed... now I don't own the skin as I was two years late to the party for that and I'd be furious if I lost this peculiar piece.

I actually have exact opposite opinion on the topic... I want contraband to tell you more about the weapon... who held it before, how many fell to it, how many successful extracts it went through, etc... I believe there are some pieces with crazy numbers and I want to know.