Gene,
A microwave works great on shore power.
If all you have is battery power, it will suck the juice out of it/them very quickly.
This kind of question generally brings a flood of "opinions" regarding the "true" meaning of "camping" and how gadgets such as these somehow make someone less of a "real" camper than those who choose to use more traditional "tools".
In case that didn't make sense, some people like to think they follow in Daniel Boone's footsteps, and strive to "camp" much like he did.
Other people go "camping" with modern amenities.
To each their own. Whatever "method" of camping suits you, go for it!
Is strange though, that those who think that using modern amenities is not "old school" camping, are pulling trailers behind modern vehicles to go "camping"...
The real issue is that everyone has a different opinion about what "real" camping is, and there can never be a definitive definition.
So,
my opinion is ; if you use and appreciate a microwave at home, generally camp where shore power is available, and have space for it, then why not?
I have one. I do not have it built in because I just don't have enough space and because we do not always camp where there is shore power.
The small ones are not very heavy, are easy to transport, and can be used outside on a table, stump, or wherever.
In other past trailers, we have had them built in, and appreciated them very much.
Cooking your dinner in a microwave is fast, easy, and allows more time for other things when you are camping.
We save extra meals during the year and freeze them. When we go "camping" we bring them along and use the microwave for a fast, easy, good tasting meal.
They also cook other, fresh food quite well.
Of course we could slave over a campfire, a gas stove, an electric hotplate, or other type of heat source, but we choose not to.
Rob, (not sure if I qualify as a real camper

)
Waiting for "someday" will leave you on your deathbed wondering why you didn't just rearrange your priorities and enjoy the time you had, instead of waiting for a "better" time to come along...