The Cheese Test (youtube link) is a great way to visualize this. If the food doesn't rotate, you end up with hot and cold spots.

(This was just the first video I could find of someone performing the test for people who hadn't heard of it, I didn't listen to the video, only confirm that that's what they're doing)

Yes, it does. Without the plate you will get hot and cold spots where the waves interact. If you don't have a rotating plate you should be manually rotating the food, unless there's some new tech I'm not aware of.

A microwave works by bouncing microwaves around the interior. Since the shape of the container doesn't change neither will the path that the bounced waves take. This can lead to hotspots in what you're reheating.

To mitigate this you have a few options:

• move the food around in the container so that different parts pass through different hotspots over time (this is what a tray does)
• interrupt the microwave path via a "stirrer fan" that sits below the microwave floor (this is what tray-less units use)

Both approaches redistribute the hotspots to maximize even heating. The efficacy of either approach will come down to the specific design of either unit, but a tray-less unit can be easier to clean, and with fewer moving parts exposed to end users can be a good option for commercial/high user count settings.

Each design accomplishes the same task of relatively even heating with few hotspots.

As others have said, microwave ovens create standing waves with regions of higher power (hot spots), which unevenly heat food. If you want to see this for yourself, Scientific American has a kids project for measuring the hot spots in a microwave using chocolate or marshmallows. There’s also a bunch of videos on YouTube of people essentially doing this same project.

As long as you don't put it in the center, yes.

It makes the heating more even. The microwaves aren't uniform inside so rotating helps even things out.

I had a microwave that moved the plate side to side which worked really well for heating anything solid, but heating liquids usually resulted in a mess.

https://youtu.be/OyTmJX_TC84

Here's a (trained electrical masters) putting metal in a microwave. I don't remember if its this or another of his microwave videos in which he warms up the cardboard box and looks at it with a thermal camera.

Or maybe it was a veritasium microwave plasma video where they show it i can't recall

Do they still make non rotating microwaves?

At least one brand now has a newer design that rotates the microwaves themselves to better distribute the energy. It's a bit pricier than the standard models.

I had a square one so without a rotating plate, IIRC it was the microwave emitter that rotated instead. If that is plausible, I sort of doubt it a little now.