non-MTB as with flat bars?
 

What is stopping me from using a non-MTB (like an old Raleigh) with flat bars? What about flat bars that are raised up?

Something about frame geometry?

Nothing is stopping you. Note that if you're talking of changing from drop (road) bars to flat bars you'll need new shifters and brakes levers. Take care also that the new bars you get have the same clamp diameter as the ones you're replacing or you'll need a new stem too.
You may want a different length stem to get the bar position comfortable.

nothing but your imagination. provided you can reach the brakelevers and shifters while riding safely. I changed lots of bikes from drop bar tenspeeds to flat bar or 2 or 4" rise bars. you can change just the bar and brakelevers or the bars, levers, stem and shifters. lots of hipsters do it!

Nothing. It's done all the time. There are a bunch of threads here on converting drop bar bike to flat bars and vice-versa. A search should find them and they will point out the problems and solutions. Mostly the inhibitor is cost if you want to convert an existing bike since some of the major components like shifters and front derailleurs aren't interchangeable. If you are starting from scratch, no problem.

Consider mustache or upright bars. More comfort.