The original DOOM levels are really quite easy, even with keyboard only. However, if you are not used to playing keyboard-only, you will feel somewhat handicapped by that.
Once you go to DOOM2 and the 4th episode of Ultimate DOOM, and then Final DOOM, things start getting quite a bit harder; however, it is still perfectly manageable with keyboard only. All of the original levels in the original games are. It is when you go to the user-created level packs that you find some really hard ones, for which keyboard-only can become an insurmountable handicap.
The fact that the game can be difficult despite “dumb” straightforward enemies shows that good “smart” AI is not the only way to make a game challenging. Early FPSs like DOOM, Quake etc. (and similar concept games like Serious Sam) succeed mostly by presenting overwhelming numbers of tough enemies. Many modern FPSs will put you against smaller groups of smarter enemies instead. These are just different approaches and personally I don’t find one better than the other – it depends on how well a game implements whatever approach it chooses.