Can a built-in microwave be replaced with a "regular" one?

In theory you could, but sometimes the built-in one is also your stove light and exhaust vent too.

it could be done, but you would have to make sure that the shelf you use is properly mounted to support its weight. (don't use wall-dogs)

built-in microwaves come with mounting brackets in the back to attach to the studs in the wall. to be honest, i've never seen one that didn't mount from the back.

if the one you have is set up differently, with a shelf to sit on, then any microwave that fits in the space will be fine, assuming there are no vents that need space around them.

You could build a cabinet or shelf and set the microwave on top of it...unless...it is above a stove. In that case you need a range hood microwave.

Some are mounted to studs in the wall,but if there is a shelf for it to set on,i don't see why it won't work.

Yes ……..with the caveat mentioned by Flying Dragon.

I have done it a few times………. just make sure it has room to breath

Yes, basically, you're right. The issue will be the size of the replacement - will it fit?