Can a power amp have too much power, risking damage to a speaker?

I've been playing electric bass for decades and I have a couple of pro bass amps (15s, 12s, mondo pro sub) and one learns that there's obvious limits on how loud you can play before the speakers get annoyed. Is this too basic? Over 6 maybe? Electric Bass teaches an interesting tone exercise.

Note that any tube guitar amp from a 5 watt studio amp to a 100 watt whatever will often be used overdriven with distortion into the speakers for DECADES with no harm done. If people are lame enough to drive their delicate little home stereo speakers to the edge with a high powered amp (especially a solid state one) there's little to be done for them.