Never mind Doom, I had a weird version of Quake running on an iPaq almost 7 years ago. I can only imagine it's come along since then.
The reason I abandoned it? How on earth do you control Quake with a stylus? Not easily is the answer. But fun for 5 minutes to find out.
The reason Apple don't want this is purely because it's the thin end of the wedge. Allow a C64 emulator, allow an Amiga emulator, allow a Game Boy emulator -> Megadrive/Genesis -> Saturn -> N64 -> PSP etc - Wii??
OK there will likely be a natural hardware barrier at some point along the chain, but you can bet that Apple have shot themselves in the foot by being guardians of the software gate, and therefore leaving them open to the inevitable lawsuits. I suppose it's also a revenue loser - you need to get a special "licence" (read money for Apple) to develop for the iPhone. This C64 emulator technically means anyone can be a developer.
Granted, as mentioned above, I doubt you'd get many people relishing the prospect of digging their software out the loft, seeing if the C90's have stood the test of time, and typing it on an iPhone keyboard. Frankly I struggle to write a medium-length email on one. Just tried it:
10 GOTO 20
10 GIRO 20 with the helpful autocorrect