Can birth controls be taken solely to prevent period cramps?

Doctors prescribe birth control to treat lots of conditions. I use mine continuously so I never get my period. That completely eliminates the cramps. It serves two purposes. Not only do I not have to worry about getting pregnant, but I don’t have to deal with periods at all. No cramps, no moodiness, no pads or tampons. It’s a win-win. 

You bet. When I was a teenager, I started the pill when I was not yet sexually active. It lessened my cramps enough that I could manage.

A generation later, one of our daughters did the same, for the same reason. Her dosage of the active ingredient is a tenth what my dosage was.

Absolutely. Birth control is taken for a number of isolated problems with hormones and pain, not just to control not having babies. My sister took it to control her acne and I took it to control my really bad PMS. We weren't even sexually active when we started it. Many women will take birth control for different reasons besides the obvious. 

yes that is really bad

Yes, it's one if the reasons it is prescribed.