I was wrong thinking it pointless.
The pet detects things it can pick up in a radius disregarding obstacles and pathing. Then it paths correctly to anything it detects.
So in those dungeons with interconnecting rooms, the pet actually will go all the way around through several rooms to pick up something you see on the other side of a wall, if a valid path exists.
Although they can’t open doors and go through obstacles on the way, so that would stop them cold.
Also, they actually need time to run over and pick things up. So in content where you’re literally steamrolling through pack after pack of trash, using your mobility skill to quickly reach the next pack before the previous pack has even finished dying, then the pet will keep up with you first and foremost, and leave things on the ground.
So it’s got its limitations, but still very useful most of the time.