Item collection and management is a core part of games like this. Without it, this would essentially just be a game like Call of Duty or Battlefield but with a whole shitload of more items.
Honestly, without encumbering the whole game breaks. Want infinite caps? There you can just sell the tons and items on your person. Now you can hold 999 ammo of every weapon that you bought with the tons of sold stuff. May as well just carry every weapon while you're at it and a lot of replacement power armour parts. You're basically a walking army. There's no longer any danger. Defeats the purpose of the genre for me, which is why I don't use the console to hack my weight limit. Situations that would normally make me go "ah!" would then be nothing - there's no potential for panic, no point in strategy, no point in having a play style that suits you.
None of this is even remotely true.
For one, each vendor has a limited supply of caps for trading. You can't just dump 10k worth of gear and walk away with all that money. Most, if not all vendors I've seen so far (at level 29) have under 1000 caps, often closer to 300.
Ammo already has 0 weight, so nothing about removing encumbrance changes that.
I'm not sure how you get to "nothing makes me panic" just because you've got a bunch of guns. With encumbrance as it is, it's trivial to carry enough guns of each type to easily deal with each situation in the first place. You still have to fight enemies, deal damage to them, and avoid it/heal yourself. Encumbrance changes none of this.
What it *does* do is mean that sometimes you have to spend time deciding what new shit to pick up and what to leave. But it's almost never an interesting choice, because other than the "junk" items, it's abundantly clear that you've got no reason to grab every piece of armor off of enemies in a given area.
I maintain that unless you actually find looking through a menu determining what to drop and what to pick up to be interesting, this mechanic is meaningless and just makes more busy work and time I'm not playing the fun parts of the game.