Some ICP systems do use lower frequencies, down to about 500 Khz - and I recall seeing some systems operating in the sub-100 KHz range. In fact, lower-frequency drivers have a few advantages; the paper
Xu, S., et al. "Low-frequency, high-density, inductively coupled
plasma sources: Operation and applications." Physics of Plasmas 8.5
has a good introduction to the effects of different exciter frequencies.
Miniature ICP systems running at 50+ MHz are also seen in the literature.
Insofar as I've seen, the main rationale for 13.56 MHz specifically boils down to availability of off-the-shelf high-power generators and matching networks in the ISM bands.
2.4 GHz plasmas are also common; plasma lamps are a striking (ha!) example of this. This seems to come down to a matter of terminology; microwave coupling effects behave somewhat differently than a simple LC-tank, so "RF-excited" makes a bit more sense than "inductively-coupled".
I don't know nearly enough plasma physics to say why 13.56 MHz is more common than 27 MHz, however.
60Hz plasmas aren't really possible, as you need the electric field induced by the alternating magnetic field to be sufficient to ionize the gas.
The book Fundamentals of Electric Propulsion (pdf warning) discusses this at length in section 4.5.