Why do speakers improve with more powerful amps?

So some people here would like for you to believe that Signal to noise ratio, Load on the power supply, ‘Q’ of an amplifier and probably a dozen other Electronic FACTs about amps has nothing to do with how they perform. Yes we have plenty of people here that make unsupported outlandish statement trying to make themselves s look like they actually know something about Sound reproduction. Talking about arbitrary factors that in them self have nothing to do with the argument. Try understanding what ‘HEADROOM’ is before opening your pie hole. And don’t be offended, I left out the juicy comments, but needless to say these types would have you believe that ALL of the specs published on your equipment is useless information.

@Phusis

This shows how easily it is to ignore the Facts of the subject and keep on trying to reinforce the idea that clipping is the ONLY place that headroom affects. Clipping is only a minor concern is is the LEAST of the actual AUDIPOPHILE reasons for having overhead.
Yes you can power a pair of headphones with a couple of well designed watts of power but you won’t be powering a set of Maggie’s with only that. You are mixing apples with oranges IF you think there is not a high level of sound quality in reference here. Or as I said before would you expect audiophiles totally ignore ALL of the statistics published about the Amps they are discussing or buying.
IF you take a lower powered Amp, say 10 watts, running at .5% distortion and run it at 5 watts what is your distortion level compared to a high powered Amp, say 100 Watts and run it at 5 watts output, with .5%. That is not .5% at 5 watts but IS .5% at the capacity of the amp, or at a designated % of output. With a higher wattage capacity you can run the distortion right down to the floor. That is just one of the factors to consider.

Possibly if I make a comparison to mechanical engineering. A simple street car capable of 150 HP putting out 100 HP is going to be under far more stress and pushing harder on every last component in it than a muscle car capable of 500HP putting our 100HP. The muscle cars is barely idling and not under ANY stress.