You're not going to win a high-speed chase driving an MRAP. As officers don't receive training in how to properly operate them, they're actually more likely to injure themselves by rolling one over than to ever have a legitimate law enforcement use for one.
MRAPs are expensive, they chew up roads, and they roll over at the drop of a hat. They are useful for one thing: protecting the occupants from explosive devices.
I actually have never heard of a case of someone throwing pipe bombs at police in pursuit. I would be quite interested in reading more about the incident.