I believe it works as it does because springing the door trap is a result of a player-initiated action—cats don't open the doors by themselves, as opposed to stepping onto ground traps. So if anything, it does make sense that it is attributed to the player.

Whether I like it, that's another issue. For cats, this isn't too much of a problem. Minions, however, instantly become hostile (at least in my admittedly not very rich experience) and can kill a Bard or a Necro sooner than they'd be able to pacify them. So something could probably be done about this, but at least w/r/t cats it seems to be working as intended.

You can also order companions to kill them for you. A player-initiated action, yet it isn't punished. And I like having these different resources for dealing with cats, other than simply outrunning them, locking them in a room or getting them killed in Dwarftown or wherever.

My preferred method is to create a trap, preferably the boulder/collapsing ceiling one and just guide the cats over them repeatedly.
Seems like a pretty straightforward player-caused death, yet it's not penalized.

This strikes me as very inconsistent behavior with the Door trap example.

The real inconsistency is between floor fireball traps and door traps. Triggering an unknown floor fireball trap does not give the PC kill credit, but triggering a known floor fireball trap does. The PC does not receive the same treatment for door fireball traps - they get kill credit regardless of whether the trap was revealed or not.