You'd have to be careful implementing a game like this, because the slightest mis-step could send the game into a fail state. Even things like saving and loading, or subtle differences in processor speeds between users could render a scenario solvable on one player's system but impossible on another's.
It should be noted that this is already an issue for some Flash 2D collision engines, and the solution among flash developers is generally use the most advanced physics engine possible, dumb the graphics down as much as possible so you can devote more processor time to physics, make your world as simple and self-contained as possible, featuring only enough physics objects to depict the important gameplay elements, and do a hard reset at the start of each level.
In other words, don't expect this in AAA first-person shooters any time soon. Mainstay features like saving and loading, ragdoll corpses, large levels, and outdoor sections would all cause problems. The best we can probably hope to do at this point is a game like Portal. One box, one button, a few moving objects, a definite Start and Goal.
If it seems like most hardcore shoot 'em ups only use physics as a special effect, this is why. If a special effect fails, the game still works.
