For the same reason that you can't make something brown&crispy by boiling it, as it turns out. Because it doesn't get hot enough. The microwaves heat the water to the boiling point, then it turns to steam, and flees the food. Once it's escaped, it gets vented out of the microwave oven. It's hard to brown meat at 100º C.
However, the previous description is not complete. Ninety-eight percent of the time, the explanation of how a microwave oven works is that the microwaves heat the water in the food. That's true, but misleading, since they don't heat just the water. They affect asymmetric molecules; more precisely, any bipolar molecule. Like, say, water. The little pictures of H2O looking kind of like Mickey Mouse with the two hydrogens attached near the top isn't arbitrary, and that asymmetry means that the electrical charge on one side of a water molecule is different than on the other side. Microwaves are electromagnetic radiation, so when a microwave beam passes by a water molecule, the plus-minus-plus-minus oscillation of the beam affects the water like a magnetic field affects a magnet. The molecule spins like a top (or like a motor!) under the influence of that field. That spinning causes friction, which causes heat.
Well, it does as long as the water molecule has something to rub against. While researching this journal entry, I found a web page courtesy of the Physics department of the University of Virginia that informed me I may have been misinformed about my microwave steamers. I blame the annoyingly incomplete "microwaves heat water" explanation for taking at face value what the "Micro Buddy" literature told me: that their plastic microwave steamers used superheated steam to do a better job than traditional steamers, since the container kept the steam in contact with the food, and the steam, being water, would keep getting hotter and hotter from the microwaves.
The University of Virginia site says this: “While it's true that microwaves twist water molecules back and forth, this twisting alone doesn't make the water molecules hot. To understand why, consider the water molecules in gaseous steam: microwaves twist those water molecules back and forth but they don't get hot. That's because the water molecules beginning[sic] twisting back and forth as the microwaves arrive and then stop twisting back and forth as the microwaves leave. In effect, the microwaves are only absorbed temporarily and are reemitted without doing anything permanent to the water molecules. Only by having the water molecules rub against something while they're twisting, as occurs in liquid water, can they be prevented from remitting[sic] the microwaves. That way the microwaves are absorbed and never remitted—the microwave energy becomes thermal energy and remains behind in the water.”
On the other hand, I've “steamed” hamburgers in the microwave and they do turn brown. Perhaps the steam density is high enough to cause friction anyway, or maybe it's water vapor in contact with the food's surface that's doing the work. I guess the obvious evidence that there are temperatures above the boiling point of water indicates that the UofV claim that you can't microwave steam is incomplete.
But water isn't the only bipolar molecule in food by a long shot. Two other common ones are sugar and fat, or so I'd been told by a different web site in the past. So I immediately found myself wondering "If fat, like water, is a polar molecule, how come I've never heard of anybody using a microwave as a deep-fat fryer?" That would allow the microwave to create temperatures high enough to make things turn brown&crispy.
Google could offer me no clear indications that anybody had tried directly heating fat or oil in their microwave.
But first, a short break. There are a couple of different "stupid questions" on the UofV web site, questions submitted by people who clearly have a very poor science education. Here's my favorite one so far: “I have a friend who refuses to stand in front of the microwave oven in his kitchen, because he feels the ‘nuclear waves’ leak and will cause his sperm to deform (and he doesn't want ugly kids). Is this true?” I am in awe. I think my favorite part is the implication that the worst thing that could happen from radiation-induced genetic mutation of DNA is ugliness.
The first runner-up goes to “I was told the holes in the front door of a microwave oven were shaped round because the microwave beam is shaped as a square. Thus, this means that a square shape object cannot pass through a round shaped object.” Square microwaves! Brilliant! Obviously sunlight is also really square; that's why window screens have square holes, so that the sunlight can get through.
The Funny But True department features the interesting fact that microwaves affect liquid water much more strongly than frozen water, which certainly explains why it's so tricky to defrost meat in the microwave. Once a part of it thaws, that spot then starts absorbing much more energy than the still-frozen parts, leading to that frozen-here-cooked-there effect. There's even an expired patent for TV dinners (sorry, “frozen convenience food”) that involve dipping a frozen food item in water to thaw the surface before microwaving (oops, I mean “surface-defrosting-wetting”), in order to cause the surface to cook hotter than the core, thus engendering crisping and browning of the outside of the food.
Now, back to the topic at hand, which is "If fat, like water, is a polar molecule, how come I've never heard of anybody using a microwave as a deep-fat fryer?" Trying to Google up the answer to that question is what led me to the UofV web site in the first place.
A 4H web site hosted at Purdue University has a web page on microwave safety says “Do not heat oil or fat for deep fat frying” but offers no explanation as to why. The Wikipedia entry on Chemical Polarity says “Examples of household non-polar compounds include fats, oil and petrol” which would seem to definitively rule out using microwaves to heat oil at all.
A counter-example comes from the Agricultural Extension Service at the University of Tennessee's PDF file entitled Your Microwave Oven: A Real Time-Saver which claims “Meats and poultry cooked for 10 to 15 minutes brown from their own fat. Foods cooked for shorter periods can be browned using Worcestershire sauce or soy sauce. Simply brush one of these sauces over the meat or poultry before cooking. Baked goods do not need a long cooking time and, therefore, do not brown.” And from Cornell University's Department of Materials Science's “Ask a Scientist” service comes this statement: “Microwave energy also heats up drops of grease to temperatures of 100°C and thus can cause the scarring that is sometimes seen on plastic utensils.” And there's even a patent for “a deep frying appliance which is constructed to effectively and efficiently use microwave energy for heating of the oil in which foods are fried.” This certainly implies that microwaves can act on oil molecules despite their non-polar nature.
In the end, I still don't have an answer. Apparently you can heat oil with microwaves. It also appears you can heat food in oil without heating the oil (as per a "microwave-assisted deep fat fryer" patent). If anybody's actually tried to use oil in a microwave to allow it to cook at temperatures greater than the boiling point of water, I couldn't find it.