Using low power on a microwave almost feels like cheating. For anyone unaware, a microwave can only be on or off, so setting a microwave to 50% power really just makes the microwave run for only half of the total runtime. A minute at 50% will be on for 10s, off for ten, etc.
It cooks way better, especially things like stews or other semi-liquidy things that tend to get hot and cold spots.
Edit: looks like my info is old considering my microwave is from 2004, lol. In 2006, LG patented using an inverter to drive the magnetron. The main benefit (according to the patent documentation) is that it's cheaper to produce. A secondary benefit is that you can, in fact, provide lower power to the magnetron. Seems like a handful of producers must be paying LG to use that method, but probably more will start when the patent expires next year.
I haven't seen one in the wild, but they are out there.