Panasonic "inverter" microwaves actually do reduce the power output. It's one of my favorite features. On power level 1 you can actually soften butter without melting random pits into it.
Unfortunately, at least on my current model, the UX to access this feature is very bad: repeatedly pressing the "power" button until it reaches the desired level. I've had other microwaves where you just key in the desired power after pressing "power", and much prefer that method.
I don't know whether Panasonic has licensed this to any other manufacturer.
Anything dense (e.g. lasagna, meatloaf, etc.) is good for a lower power level / more time trade-off. It will end up more evenly warm without the edges exploding. I usually use power 3 or 4 for these dense dishes.
Unfortunately, at least on my current model, the UX to access this feature is very bad: repeatedly pressing the "power" button until it reaches the desired level. I've had other microwaves where you just key in the desired power after pressing "power", and much prefer that method.
I don't know whether Panasonic has licensed this to any other manufacturer.