The fault current that a breaker is required to be able to interrupt is two orders of magnitude larger than we're talking about feeding into the wire, and a 15 amp breaker is designed to _not_ interrupt a 150 amp load until a second has passed (there's a rating curve for this): some loads might require that much current briefly, and the wire in the wall is not going to overheat in that time (that's why the breaker has the curve that it does: to model and therefore protect the allowable heating of the wiring).

Doubly so because it doesn't even do what we want it to which would be to switch the main breaker off.