The problem with DOOM and Hexen is not simple "they use only a single SH2". They are *BAD* ports, as unoptimized as it can be.
It seems those games not only use a single processor, it seems the processor is also used for rendering, since they use custom software engines.
Also, Doom was ported straight from the abomination that is the 3DO version, and it's rendering engine looks far worse than the PC version, or even the 32X and Snes versions, even if on a slightly higher resolution.
Had they ported the game to use the VDP1 for rendering, like Duke Nukem 3D, Quake and PowerSlave, things could've been better.
As for split-screen... it could work, but at low framerates (~15), using 2D sprites for characters/items, and fairly simple levels (indoor, many corridors and some aggressive sector-based culling going on). Not sure if it would be fun enough under such conditions.