As a player, I spent most of my time finding the key to unlock some door, rather than killing monsters.

I think Doom changes with subsequent replays. After a while you start to learn the layout of the maps. They stop being mazes and start being puzzles, where you know where all the pieces are but the difficulty is in finding the optimal route to accomplish your objective.

There are many WADs out there for Doom with extra content and levels to play.