Hoarding

Essentially: You're expected to take everything that isn't nailed down.
... one could assume that in some cases you'd need to take even those.

This doesn't refer to player being able to pick up everything, but rather everything must be taken and everything will have a use, one way or another (e.g. triggering a scene, even if the item is never actually used).

Usually also means that if your inventory is empty, you've missed something.

See also: collecting (in case the collecting/hoarding itself is the goal)

Contrast: trash (cases where there's lots of items that have no use what so ever)