What’s so special about the “microwave” part of the EM spectrum, as opposed to something lower or higher? Why don’t we cook food with alternating fields of RF or infrared radiation, etc?
You can actually cook things with a wide variety of frequencies (as any radio technician who has ever experienced an RF burn can easily attest to). Kids with magnifying glasses have managed to cook ants pretty successfully as well over the years, proving that visible light can cook things as well.
At lower frequencies, the wavelength gets longer, and therefore things that are based on the wavelength, like the chamber size and the waveguides, get bigger. The distance between hot spots and cold spots gets bigger, too, resulting in a more uneven heating.
Water also has a peak of RF absorption right around 2 to 3 GHz or so, which means you get your most effective power transfer from the oven into the food at these frequencies. Have you noticed that a lot of fairly modern things use frequencies right around 2.4 GHz, like cell phones, wi-fi, cordless phones, etc? That’s because at these frequencies, water in the air tends to absorb and attenuate the signal more than other frequencies making them less desirable for communications. So when the newer stuff came along, these were about the only frequencies they had left to use. These frequencies are also pretty good at transferring energy into other materials like certain fats and sugars, so overall they work really well for an oven. A radar transmitter running at 10 GHz wouldn’t heat your food as efficiently since less of the energy would get absorbed by the food. Higher frequencies also don’t penetrate as deeply into materials, and our current microwave ovens already have problems heating up the center of a thick piece of meat, for example.
So below 2 GHz or so the oven would have to get larger and the parts larger and bulkier. At higher frequencies, the energy wouldn’t get absorbed as well, the cost of the magnetron gets higher, and the heating doesn’t penetrate as far into many materials. This kinda makes a sweet spot around 2 to 3 GHz.
Other frequencies of electromagnetic radiation may not be very practical for food, but they do have other uses. A lot of circuit boards these days have their solder melted into place by infrared heating. And of course there are things like cutting lasers which use all different frequencies of light. Some folks have even focused sunlight using mirrors, and have then used the heat generated to operate something like a sterling engine or some other heat engine to produce practical energy from it.
Thank you for the detailed and clear explanation 
So just to make sure I’m understanding this right:
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~2.4 GHz was left unlicensed because that part of the spectrum wasn’t very useful for long-distance communication anyway, because of the atmospheric water content.
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Most food also contains a lot of water, so microwaves might as well target that – because not only does that frequency range heat up water the quickest, but it also doesn’t require spectrum licensing, and doesn’t require overly big components
Followup question, if I may:
As for focused sunlight, magnifying glasses, solar collectors, etc: But those methods don’t involve dielectric heating, right? Do they just pump energy into the object without reversing the polarity of water molecules and increasing internal friction? If so, can it be said that microwave ovens are more efficient, somehow?
I read about electronic energy and quantum transitions vs dipolar polarization, but I don’t understand them well enough or know how to estimate their efficiency 
For example: Given 100 Wh of energy to cook a hot dog, would it be better to cook it with a solar collector, a microwave oven, an open flame, or does it not matter?
About microwaves, there is also the magnetron tube, the heart of the microwave generating system in a microwave oven. This is a vacuum tube in which a heavy stream of electrons swirls around in a magnetic field so that its shape resonates. That’s what creates the high frequency, and it does so in a way that is inherently easy to make powerful. I think it’s a fair comparison to suggest it is like an organ pipe or a whistle. I think the frequencies used are convenient relative to the shape of the magnetron. If we wanted the frequencies lower, this expensive part of the oven has to be made much bigger, and if we wanted the frequencies higher, the expensive part would be smaller but also not very powerful.
Though I’m going out on a limb a little bit here. If anybody else can improve or fix this line of thought, please do!
We do cook using infrared-- That’s a much older technology than microwaves, and you have a device for it right underneath your kitchen range.
The biggest difference between infrared and microwaves for cooking purposes is not that water absorbs microwaves more than infrared-- It’s that it absorbs them less. When you cook something in your oven, it’s only the very surface of the food that gets heated directly, since the infrared is all absorbed within a millimeter or less. Everything else must heat by conduction from the surface. In a microwave, though, it takes a few centimeters of food before the radiation is mostly absorbed, which means that the heating penetrates to the center of most foods.
Here is a nice PDF article which explains some of the physics of a microwave oven and why 2.4GHz is a good frequency to use.
And the wiki Microwave Oven article goes into the history of the oven.
In the 1980’s, when the FCC was being pressured to open up unlicensed bands, the 2.4GHz band was considered for it because it was already messy with medical and microwave oven utilization. So adding in other low power transmitters would not make the band any worse than it already was.