Why do speakers improve with more powerful amps?

Why do more powerful amplifiers impact speaker sound quality in a favorable way? 

There isn't an equation written that can explain why, my experience is the soundstage gets more like it was in the studio when you add "enough" power. Once you get to "enough" you can park it there and more power than "enough" is basically a waste.

Mine sound pretty good with 30 watts of class A.

Roger from Rogers High Fidelity had an interesting comment somewhere about amps operating in their "sweet spot" of sort of a median power delivery, and noted as an example that very powerful amps into efficient speakers don't get the amp into its best tone zone. Not his exact words but I get it.

It's the old DQ 10's analogy I hear in the DQ 10 group I read info in.  "You need a minimum of 200wpc 'to make them sing' " Garbage.....  Mine sound fabulous with a 40 wpc Proton D540. Sister company to the early NAD company. But it's capable of 160 wpc for music transients when called for.  That's at 8 ohms. It's all about the current it was explained to me. I don't listen loud....so no need for a heat producing beast.

I agree with the posters who indicate "it depends". My current Revel speakers are rated at 6 ohms with 87db sensitivity. They were initially being driven with a 50 WPC Arcam and I needed to push the amp pretty hard to get the speakers to sound their best. I switched to an 80 WPC Cambridge Audio amp and the speakers came alive. I noticed it especially in the lower frequencies. But there was also the matter of synergy. The CA amp, being a little more forward sounding, meshed better with the laid back sound of the Revels.

I had been using the Arcam with a pair of Paradigms that were rated at 92db at 8 ohms. That was another great synergy system. 50 watts was more than enough to make those sound great. 

It depends.