Quality inversely related to power output?

Agree & disagree.

Disagree: on the strength of absurdity. Low watt amps are NOT better than their hi powered brethren UNLESS they sell for about the same price... in which case one MAY assume that there is disparity in quality.

Agree: it is much more complex to execute a high powered amp at the same quality level as a lower powered one -- in fact, certain topologies are not available at all (example, 500W SE no negative or positive feedback, local or global).

Agree 2: as a result, it is disproportionally expensive to produce hi-powered amps of exotic quality & design (say, for example, a 500W deep class A). So these are rarely offered.

Disagree2: again, this is not a rule but, rather, a generalisation statement of what is GENERALLY available in the market. There are marketing reasons for this state.

Not true. As Gregm says - it is simply more difficult and more expensive to build more powerful amplfiers with similar performance to lower powered amps.

If your only measure of quality is distortion then stick to headphones.

As far as I am concerned, dynamics and ultimate SPL output is also quality. If an unamplified piano or drum set can produce north of 110 db SPL on transients then the low distortion qualities of an underpowered system is rather a mute point - as it can never realistically reproduce the range of natural sound of musical instruments in the first place...

I am of the "first watt" camp.If you don't get the first one "correct",then the rest doesn't matter.
It is much harder to get multiples to act as one/two.That being said,you'll never drive 86/88db efficient speakers with 3W to a desireable level.