Yes, traps in Morrowind were all magical of some sort - or at least, they appeared to be.
Which is probably why I like the idea of containers and doors that are simply trapped, not locked. Sorcerers are perfectly capable of disarming a trap without using a key or a probe - that's what mages in Morrowind could do with Telekinesis. So it's logical that they trap containers/doors without setting up a way to disarm it again, because they have their own way of dealing with that.
As for the reason why they should not also lock the container/door if they already go through the trouble of setting up a trap... maybe they lost the keys?
Other than that, there are doors that don't have keyholes (secret passageways or simply strange doors).
I don't think it should happen very often that a container/door is only trapped, but having the option would certainly be nice, and some situations might benefit from it. I guess anyone can see that a door/container is locked in some way, but a trap, especially a magical one, might not be detected so easily - nasty surprises, here we come!
(Based on the assumption that you can only see that a door is trapped by making a successful skill check.)