Just to be fair to the argument on both sides, the circuit breaker makes a very lousy current limiter. It is mechanical and hence can have slow response time. The key here is that its slow response time has been incorporated into the rating of the wire that feeds from it. Here is a generic graph showing that:
See how the danger line for the wire is well clear of the graph. If you look at the 14 amp romex for example, that is one beefy cable. So while the wire will certainly warm up some if there is a catastrophic short, it can live through that until the breaker opens per vertical axis of the above graph. Imagine how much power it takes to heat up tens or hundred+ feet of cable to the point of the insulation igniting.
There is a secondary problem in that there can be arcing across its contacts when it attempts to open. The higher the current that it is trying to interrupt, the worse this is. The arcing can weld the contacts shut and not let it interrupt the circuit. Fortunately breakers are design to withstand many multiples of their actual rating using various methods like putting special gas inside it. But whatever that rating is, it is not gazillion amps.
A quick story on this. A "friend" (
), cut through a live romex wire with electrician pliers while holding a part of it. Massive spark was the result and it completely pulverized the cutting jaws of the plier. Clearly good bit of juice went through the wire. But the wire was as cool to touch as it was before the short. So the system works. It is overbuilt for the purpose to keep folks out of trouble, including my friend here.
BTW, it is for this reason that you never, ever, want to rely on the circuit breaker to protect your gear. The breaker is there for one and only one thing: to protect the wire. It is too slow to protect any sensitive equipment downstream. They need to have their appropriate fuses or they can catch on fire, etc. and the breaker not doing a thing.
So concluding, the reaction time of the breaker is not instant. But it is fast enough to protect the wire.