Why do speakers improve with more powerful amps?

I think speakers reflect the amplifier, in the last three years my speakers have remained (Sonus faber Olympica Nova V) and have used 3 amps where the sound difference has been dramatic:

1. McIntosh MC300
2. Moon 400m
3. Moon 860A v2

My current amp is the ‘least powerful’ at only 225 watts into 8 ohms and it’s the fastest, most dynamic and detailed amp of the bunch. 
 

a good amp is a good amp - watts/amps are simply ways to measure but there’s most to the design and build then just 1 measurement. 

Let’s take a look. You have an MC611 and a 1.25. Their sound signature is quite similar but the dynamics, bass and everything else imaginable to your ears is galaxies better with the 1.25. While I don’t know the technical reasons why, I know for a fact it is incomparable better. So in this case, the one watt story and why you would need another 1199 of them more makes perfect sense.

@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.