I think you are underestimating the load involved
Looking around on the internet, you find things like these:
https://www.electrodragon.com/product/4000w-high-power-scr-electronic-volt-regulator/
They are ment for resistive loads, so spot on!
Maybe not quite the type of equipment that would be used, but hey.
The product page lists an efficency of 90%.
That is a heatoutput of over 300W for just the switching.
Means for example for 3500W max heating power you'd have to go to about 3900W supply power.
The rest? Just blown into the kitchen.
Even going by the way more optimistic figures in the data sheet related to that item, we would still have up to about 20W of heat to dissipate.
Sounds awesome, right?
That is still the power of a modern laptop CPU.
Looking at computers like Intel's NUCs, you know what it takes to cool these with ambient air and the limited space.
Then you add the fact that you already have an insane heatsource just below your electronics, and it won't go well given your Tmax is 125C for basically all triacs.
So on the only way out is to design some really good cooling solution.
Which again means high development cost and high production cost while still having medium return.
There is a reason that there has been a number of instances where peoples ovens just died on self clean.
Electronics hate heat.
And one look at basicly any high power switching application shows the heat involved.
Most inverter boards for washer motors (I know these use most likely MOSFETs, but that really dosen't matter much in regards to their efficency profile) have heatsinks on them.
Yes, most of them are cooled passivley, but they only have to operate in ambient temperature.
Now again multiply the required output by 6 and raise the temperature around the device by 60C or so while maintaining a slim construction and you either have to compete with one hell of a cooling solution or just don't do it at all.