I beleve that the main problem when you want to run a "Doom-like-game" on an amiga is:
All the 3D functions (texture mapping and so on) make a chunky-bitmap insted of a bitplane, and because of that the amiga processor has to spend ALOT of time in converting it from chunky to bitplanes so the amiga chipset can handle the graphics. I think it is about 60-80% of the processors time is/can be spend on this conversion.
To put it in another way, then it should be possible to run "Doom-like-game" in full speed when comparing the amiga processor to a PC processor (x86) if you have a chunky-pixel graphicscard like the CyberVision, Picasso BVission and so on. (The game has to support thoes graphics cards! otherwise it will still make the conversion a then a reconversion to the graphicscard!)
ps: correct me if I'm wrong :-)