Why do speakers improve with more powerful amps?

@riie MC611 is a lesser quality amp than amp than the 1.25 - compare the MC611 to a Boulder 300 watt amp and I think you’d be surprised on the sound. 

Why do speakers improve with more powerful amps?

They don't. It's a common misconception that fails the common sense test. If that were the case, a Decware Zen Triode, at a whopping 2 wps, would sound lousy. 

It's baffling why so many people believe such ridiculous things. 

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.