Those two facts are (partially) related.
You could take the Genzler, put it in a much larger enclosure and add a passive heat sink, and you would not need a fan any more. We've had these in the past.
When you shrink something to the minimum of what is feasible, among the first things you'll have to do away with is passive cooling because that needs room for the components and extra room because those components need air around them.
Even with class-D being highly efficient, when you make a 350 watt amp, you will have to anticipate that people will run it on full, and it needs to survive that.
Constructing a worst case scenario,
let's say the Genzler has a true power rating, and at full, it puts out 350 watts, and you play a piece that completely consists lots of long, low notes played legato, so there is very little dynamic content, it's basically full-on all the time.
Grabbing a number out of thin air, I assume the amp has an efficiency of 90%,
then it'll pull 388 watts from the socket and those extra 88 watts will mostly turn to heat that needs to be taken care of.