I like big butts!
Doom's keyboard controls are ideal for maps where you mostly run forward or navigate quickly without the need to aim precisely with split-second accuracy at all times.
In fact, there's at least one record-holding speedrunning (sorry, can't recall the name) who's well-known for being a pure keyboarder, so perhaps for certain particular situations, pure keyboard controls have an advantage. But no matter how good they are, the mouse comes as an upgrade to the keyboard, allowing almost all of the speed + uncanny aiming accuracy + positioning speed.
IMO any control scheme has to make a compromise between ease to use, obtainable accuracy and achievable speed.
"Ease to use" is hard to quantify, but I'd say it's about using the less different devices with the most explicit inputs, so mouse + keyboard would "lose" this round to pure keyboard, pure mouse and pure gamepad, as it map controls very compactly in two devices: the keyboard & mouse WASD config looks a lot like a Mode 1 RC flight controller ("throttle" and "aileron" to the left, "pitch" and "yaw" to the right). Accuracy and speed are the best with this config, which is why it kicks so much ass in MP.
On the converse, a gamepad is much more explicit and diluted, with separate levers for pitch etc., which might be less confusing for a newbie (thus "easier", if you don't need it), but not as efficient (have to reach for an extra control every time). It might come natural for console players, but because of the way it maps controls, it sacrifices speed and a great degree of accuracy.
Keyboard-only is an intermediate situation: it allows mapping certain controls efficiently (at least for styles of maps that allow "driving" through them), but it's tricky to find an efficient strafing scheme that can compete with mouse + WASD. IMO, in most situations it would beat the gamepad on learning effort parity. It has a bit better "ease to use" compared to mouse +keys, but can only match its accuracy and speed under certain fairly restrictive conditions.
Mouse-only tries to map way too many controls in one device which lacks enough inputs to begin with, plus it maps a critical control (fw/back movement) to an unstable axis (the y-axis), making it fidgety and imprecise to work with. It's really a last-resort control method, if you happen to have just one hand (and yes, I know the unfortunate implications behind this...). It's neither easy, nor fast, nor accurate (except maybe for maps where catwalking with pixel-width precision is critical...aka none of them).