Why do speakers improve with more powerful amps?

OP,

There is a lot of contradictory and attitude coming from different camps in this string.

It sounds like you generally understand. A higher powered amp (in current) with the same sound quality will typically sound better than a lower powered one. This is particularly true with solid state amps. Solid state amps react incredibly fast to demand… which can deplete their reserves (not just for bass). So you get greater solidity and ease. Tube equipment is slower (but often much more realistic sounding, and less prawn to run out of power).

Speaker designers are trying to go for the very best sound they can achieve, and a cone that can snap back quickly generally means greater accuracy… but to move it, that required more power.

I quickly learned in the late 70s that if I wanted to enjoy the current guzzling electrostatic speaker (a different reason for needing massive current) I needed to most muscle available (at the time Threshold s500)… which I took out my first loan to buy.

I am now using a tube amp in triode mode with only 70 wpc. While it generates 140 wpc in linear mode… it sound better in triode mode because it sounds more musical and natural. Then my speakers are 90db. You can see my system under my user ID.

I remember when I had my Adcom setup GSA 555-2 (250 wpc).  They were bridgable mono's, so I purchased another one of the same amps and series.  The end result?  My system sounded like a PA system.  Loud as hell and very unpleasant (sibilant).  I still like a lot of power because I like to feel the orchestra or the rock band playing, but now it's with tubes.

@ghdprentice 

Very nice main system and the space, lots of audio research very Tubi. The room looks dead quiet. Another world.

Also like the Tiffany lamp, and really love the doggie.

Use of the meridian processor and speakers for Home theater is interesting, not many of these systems are out there.  I like the idea of separating the HDMI signal which I believe is how it works. Wish more systems would do that sort of thing. 

I'd love to answer but there are so many variables it would take a small book. But all things being equal my friend George Bischoff who built triode tube amps(Melos) with over 400 watts/channel always said a good big amp will beat a good small amp every time. Notice the word good which encompasses many things. But it will always include a superior power supply which is costly and can be compromised without affecting standard specs. 

"headroom" is also a marketing term.

Utter garbage! Don't make wild, unsubstantiated assumptions. If you don't understand the term, it's not that hard to find an explanation. You don't even need a book. Just a computer and browser, so there can be no excuse.