I've seen them installed like this where the other thing it contacts is not suitable for mounting it, like a bathtub or another door.

Ive seen it both ways. Not even sure which is more prevalent.

It should be mounted on the wall. You can bend down the spring to go under the door and hold it open, if it's installed correctly.

It'd make a lot more sense to do it that way.. if that weren't likely a hollow core door with 3mm of wood and maybe some cardboard strips for "structure".

Most of ours are on baseboard, but a few are on doors where they'd hit closet door or something mobile, so the door gets the stopper instead of the other part that moves.

Now that I think about it I don't think I've ever seen them on the wall