Oddly, I am still used to play DOOM (and other oldschool FPSes) with the keyboard only. Although I have been playing newer FPSs as well, so I am used to using the mouse in general. But I guess that in every game the scheme that feels the most natural to me is the one I used first, and for DOOM / Build Engine games it was keyboard only.
The original levels were designed before usage of the mouse was prevalent. They are really doable with the keyboard just fine. I imagine that many of the newer "massacre-fest" mega-wads (Hell Revealed and everything inspired by it) would have segments that are very difficult, if not impossible, to do with keyboard only, because you simply cannot turn fast enough to meet the press of the insane number of monsters.
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