1). Low frequency light is inherently safe
Microwaves are huge. They do not fit through tight spaces and they do not have penetrating power. You can see visible light coming through the holes on the door of the microwave when you look at your food, but those holes are small enough to stop microwaves from leaking out and killing you. The walls of the microwave oven do not need to be thick because microwaves just bounce off metallic surfaces. You can even test this by trying to heat water inside of a steel cup. Even after 5 minutes that water will be just as cold as when you put it in; the steel cup reflected all fo the waves.
2). More things are capable of absorbing microwaves
Microwaves cause the bonds in organic molecules to vibrate, which causes heat. This seems to be particularly true for things with lots of oxygen, such as water, sugar, and butter.
Other parts of the EM spectrum do different things. For example, radio waves are very difficult to absorb. Higher up on the energy scale is IR. Most organics will absorb IR, but only in a few specific places; this is why IR is used to identify organic compounds. IR would probably not absorb enough to be effective. Next is visible light. If you had 1000W of visible light in your microwave, it would be like looking at the sun; how can you even tell if your food is done? Next is UV. UV mainly applies to things with pi bonds and lone pairs; that would be things like sugars, fats, and proteins. UV would probably work, but UV is smaller than visible light, so it would easily go through those holes in your microwave door and severely damage your eyes when you look at the microwave oven. Higher energy light will keep doing the same thing as UV - cause cancer and permanent eye damage.