Filtering and searching would help, but if you’re looking for an item that you forgot the name of, a search doesn’t necessarily do much.

Keywords are the answer. If the player forgets whether the healing item is called "medkit", "first aid", or "bandage", just let them search for "heal".

Some games use their inventory system to limit the player, making sure they don’t start a level with enough health potions and grenades to cheese every fight.

That's better solved by just not giving the player that many to begin with. Some games adjust their item drops based on what you already have, so if you're running low on pistol ammo, they'll give you some. If you already have five grenades, you won't find any more until you use some. That achieves the same goal without limiting your ability to pick up different types of items.

In survival games, a finite inventory sets the gameplay loop: you go exploring/mining and then return to base, drop off your stuff and head out again. It makes your base valuable, if only because that’s where you keep most of your resources and moving would be hard.

That's exactly one of the things that I hate about limited inventory space. It's effectively the same as hauling vendor trash, and that's something that I view as an unnecessary interruption of gameplay. "You've had fun killing mobs for five whole minutes, time to do a chore!" Yeah, no, that can fuck right off. All the way off.

I played a Minecraft mod that gave me an effectively infinite inventory. I went mining for so long that it started to feel like an awful slog.

But that was your own choice...?