Is powerfull Amps only for low sensitivity speakes?

I've run speakers that are 92+ db sensitivity and greater with solid state amps that were well over 200 watts per channel with no problem at all. Just be sure your volume is turned down.
The opposite scenario is what you want to avoid; an amp with too little power.

+1 Not that I ever use high sensitivity speakers - the refined ones that I like all seem to be low efficiency ones: both systems (Quad 2805 and Harbeth P3ESR) are about 83 dB, apart from the 86 dB Wharfedale Diamond 9.0 in the bedroom.

"You can never have too much amplifier power".  A good audio rule to live by.

I'll be the outlier here, so far...

Had a (nice) guy in my audio club who had a monstrous pair of monoblocks that ran as hot as hades, yet listened at mostly librarian levels.  Looked like the guy who own a Ferrari but drives around at 25 mph.  What a waste of money, space, HVAC, volume / loudness, potential, guts, and electricity...  Always wondered, what's the point???

Ideally the more power available the better, the higher sensitivity rating the better but there are good reasons not all speakers are 100db+ and there are plenty of 3-4 watt power amplifiers that are worth listening to. Ultimately the more power you have in reserve not being used (duty cycle) the more headroom you have for dynamics and this also relates directly to the power supply. Think of an 18 wheeler going 50mph vs a moped going the same speed. One is giving it everything (which translates into distortion in audio) while the other is barely breaking a sweat. When you have 200 watts available but your speaker is putting out 3 watts- which is a decent listening level- that extra 197 watts is just sitting there like a heavy duty reserve power storage not being used so when a loud cannon blast comes along the level will increase dramatically as it would in real life. That's my best explanation. Ultimately some very refined and superb speakers will only have an 86db rating due to drivers used and crossover design but that's by no means any way to determine the quality of the speaker. Amplifier watts are used far too often to determine quality when in reality the old rule applies- pick it up. Is it heavy? That means it has a proper power supply and although that's only a start, it's a good sign.