It's a good keyword to search for a microwave that isn't the same $15 hardware as all of the other ones.
I don't care about the variable power, but found an "inverter" microwave without the rotating plate, which cooks evenly without it of course. It has more internal space and is easier to clean.
A lot of electric ranges do the same thing, which is incredibly annoying. I mean, the 60 Hz is right there; why are they blasting in 10 second intervals?
If so, relays have significant switching times and limited cycle counts due to arcing - especially under load. Enough that sub-second switching times will wear them out pretty quickly, and also be annoyingly loud.
At the power levels we're talking about for a resistive stove, solid state is expensive. At the voltages we're talking about, it's also not trivial to do in a reliable way using solid state techniques (240V RMS =~ 340V peak).
SCRs are used for industrial stuff with much larger loads than a consumer stove. Regular relays definitely are the wrong thing to use for high speed switching though.
Thanks for the pointer - a quick google showed SCRs in the 30+ AMP 240 volt range (minimum useful for even a small range) at well over $1k. That sound about right?
In addition to everything else people mentioned, high power microwaves tend to cause pockets of steam inside food which explode and make a big mess all over the interior. By dialing down the power level on an inverter microwave, you eliminate the chance of that happening. This did not always work on the old cycling microwaves due to the long duty cycle.