I avoid using the microwave when I can. Its hard to think about what people did before microwaves, because we are so accustomed to them. How did people heat things at all back in the day? Maybe it was all cold pizza and chicken and baloney sandwiches in your lunch pail. I was too young to know.
I think there are few items that can't be successfully heated on the stovetop or toaster oven. It just takes some skill to do it right. But remember: the mushy, soggy microwave effect was something we all had to get used to, as well, and after a few years we all figured out ways to minimize the loss of quality with microwaves. Same is true for the stovetop.
Most things are cooked already (hence the term "leftovers"), so you don't want to overdo anything. So depending on the item, I often just put a pan on the stove, and toss in a small amoutn of either oilive oil or water. Sometimes I'll add a lid so that it steams nicely. The water or oil keeps it from burning and refreshes it.
Often, I'll mix items together to re-heat in a single pan, forming new concotions I've never tried before. That happened the other day. I had some kohlrabi. I choped up the thick stem part into little cubes, and tossed them into a thin layer of water in a pan. They started to boil. I then chopped up the kohlrabi greens and put them on top--they were essentially steamed, since very little of it was actually in the water itself. As they were cooking, I decided to re-heat some turkey burgers I made the night before. I figured I'd just throw the turkey burgers on top of the kohlrabi to warm them up, since the pan wa already hot. The result? I had a nice meal of kohlrabi greens and stems mixed in with turkey, and it was an amazing combination of flavors!
I can't point you to any research, but I've heard enough about microwaves to be cautious about using them. Jury's still out, but in the meantime I'm playing it safe. Why wait until something is proven wrong to change your ways?? It wasn't scientifically "proven" that smoking causes cancer for a while, too, but anyone with common sense could have told youthat smoking seems to be something to avoid until we find out for sure. I think food tastes better and feels more right coming off the stove. No radiation or altering of the chemicals in the food making them uneasy (or impossible) for humans to process, as some people say.