Is powerfull Amps only for low sensitivity speakes?

A lot of interesting facts posted as well as a lot of interesting opinions.  Of course,  many times, Opinions turn out not to be facts, so,  I'm going to give one of each....
Fact:  Nothing says that sensitivity alone has Anything to do with the sheer sound quality of a speaker.  I've been building for near 40 years now.  This is a fact.  Well chosen high sensitivity parts can produce a high sensitivity speaker system.  Poor parts OR poor design will produce a lower quality regardless of Sensitivity. 
Opinion:  way back when,  We produced a particular speaker that was 97db sensitivity @ 8 ohms.  This particular speaker (15 inch 3 way) sounded great with Tubes and solid state,  but man,  when you put a really good big mama solid state amp on them with a great power supply,  these things reacted with dynamics like non other.  
So, my opinion, in general is:  High powered solid state amps can be a benefit to High Sensitivity speakers. 
Clear as Mud?  Tim 

So, my opinion, in general is: High powered solid state amps can be a benefit to High Sensitivity speakers.

The generalization is the problem. I often run amps of 150 watts or more on my speakers, which are 98 db. I certainly don't mind the power!

I've heard 500 watt amps on that speaker and they can't make detail. They also sound bright for some reason. I've explained why.

So I think you have to define some limits, within which what you say is perfectly true.

This is an interesting discussion.  My immediate query is why are there out there sensitive speakers and insensitive speakers?  I have no audio technical knowledge but I do know from reviews of speakers that apart from what they have in common in regard to most different brands, the approach to their design in some aspects are always slightly different in some way; its like the designer of each brand thinks he or she knows best how to create the perfect speaker.  However from my limited experience if one tested different speakers and amp with power (some oomph) in comparison with amp of lesser power, the amp with power will more likely show the individual 'talents' of each different speaker while the lesser power amp may not give the 'full sound' with some of the speakers.   

Mine are low-mid 90’s I think as far as sensitivity. 
I run them with McCormack dna-750’s. 
Only rated at 250W. But boy oh boy do they sound sweeeeet, nary a hint of distortion anywhere with my CD player. 
Never a chance of clipping, and the peaks and crashes, double bass is flawless and tight. 

One other thing to consider:
With many manufacturers, in a line of variably-priced items (in this case, amplifiers), as the designers have more money to work with, they often times put higher quality or performance in the higher priced items.  With power amps, the high powered ones, which command a higher price sometimes have better performance or features.
Back in the day (over 30 years ago), I'd say that many of the then high-powered amps did not sound that good at much lower power levels.  But I think that's a thing of the past.  I suspect that most "class a/b" amps today run in "class a" up to a watt or two; if you have efficient speakers, might be listening in "class a" much of the time.