Because if they do, it'll be "find the wee spot, scrub the puke spot, pick up the poo spot", which doesn't sound as much fun:

A computer game that turns pet hamsters into virtual man-eaters could be the first in a new breed of games aimed at both people and their pets.

"Mice Arena" is an augmented-reality computer game in which human players are pitted against a real, live hamster.

The only real problem I can see, from my own experiences with "typical" on-line gamers, is the number of complaints they'd get that the hamster was hacking.