I don't know about proper induction cooktops, but the hot plates all seem to use mechanical relays to switch power, so they're limited to far less than 16 MHz. Most seem to use regular, industrial controls that operate at more like 1-0.1 Hz.

I honestly don't think you'd want to use anything but a mechanical relay to switch 10-15 amps. Do that with a solid state relay, and you're going to waste 15-25 W in a small package that will have to be radiated somewhere.