does more power=better quality ?

No, but............

In the case of what some like to call "digital switching amps":

Taking a given module, and operating it at both the lower and upper end of its operating range, most listeners prefer the sound at the upper end of its range. Mainly because it "sounds" like it has more drive.

Since the stored charge in the supply caps, and therefore the amount of energy available on short transients, is the product of the voltage squared times the capacitance, raising the voltage makes a more dramatic effect than raising capacitance.

So, if that is your main consideration in determining sound quality, yes, there is a valid reason why it could be true.

In the case of a Class AB amp, operating at a higher voltage reduces the capacitance in the devices that determine the bandwidth and phase margin of the amp. Both of these could lead to minor improvements in sound. But only up to a point. Beyond that, the changes are negligible, and other factors enter in that make amps harder to build.

"More transistor rush / more tube rush"

What on earth are you talking about?

No, multiple devices don't need to be trimmed, although it helps to make sure that one device doesn't hog all the current. That is what all those nasty resistors are there for: to minimise those effects for guys to lazy to spend a few pennies to match them.

BTW.......there is an optimum value for the voltage drop across those resistors, but that is way off topic.