Funnily enough the sprite based enemies were a real strength for Doom compared to many of the fully 3D games that came out in the next generation, including Quake. Because rendering full 3D enemies was taxing for the hardware you couldn't put too many of them on the screen at once. In some games more than 2 or 3 would cause it to chug. So you only ever run across one or two enemies at once in the games, unlike Doom that wasn't afraid to throw a swarm of pinkies at you because you just picked up the chainsaw.

Agreed. I think "Painkiller" is one of the few games that actually managed (much later) to put a healthy amount of enemies against you just like Doom did..

Doesn't matter, to the Doom engine they are tall cubes , albeit with increasingly awful collision detection as the cubes increase in size.

So according to your definition Doom is a full 3d game, even though as a player I actually see 2D weapons and 2d enemies?

Of course it is in the "game" sense. It handles X, Y, and Z axes in game on mobs and the player, although it is selective in which mobs get the "Z treatment". Monsters are infinitely tall, projectiles aren't. It's not a limitation of the engine as much as it was a design choice, as Y-shearing was too ugly in Carmack's opinion, so it was removed in favor of a very forgiving auto-aim.

Nothing's stopping someone from adding code to render 3D models or "portals" in the game, and in fact it has already been done, with no 3D acceleration needed.