I think the closest thing we have to that game on the Amiga is Leading Lap, which I think is not that bad, using the same engine and making it more arcadee and more for aga and high spec amiga's I seen no reason why something like that could'nt be made.
leadinglap video
http://www.youtube.com/watch?v=CilB8OBvsOYalso Hunter I think is a good example of how much could be done, very first GTA stly game I played where you could get into car, tank, bike, boat, etc all in 3d and gfx and animation where pritty soild for their time
http://www.youtube.com/watch?v=A3KNeckjgfsI think Agry Birds could be done on Amiga, the gravity/physic part is only thing questioning but I'm sure I played a Worms rip off PD game that you could shoot tree over or somthing like that, it be nice if we could get a port or a clone made on the Amiga.