First-
A string can break by playing along.
Second-
Potential for the amp to go out? How about the potential for the backing track to fail?
You're not going to hear any difference if a string breaks if you're not plugged in, are you?
Yeah, the backing track could fail; a meteor could crash into the stadium; the point is to minimize the potential risk of failure. Not having to deal with amps, instrument failures, miles of extra cables, boxes, FX, mixes, and so on means there's a lot less to go wrong. Halftime shows are primarily for television audiences, not the people actually in the stands; so like it or not, the sound is secondary to the visuals.