Built in models come with trim kits, so I think not. I could be wrong.

What models are you looking at?

I don't know why you say an over the range microwave is more affordable. You can get a countertop MW designed to be put on a shelf for $120, or less with sales. An over the range microwave is more expensive than a MW designed to be put on a shelf. It's also much wider than a MW designed to be put on a shelf. And, it does not have a flat bottom because it has lights and the fan mesh screens, so it isn't possible to rest it on a shelf.

Any countertop MW can be put in a cubby hole, but OTR MWs might have venting issues since they're meant to be attached above.

I would not suggest doing that but you can expand your options to standard microwaves. You can get a trim kit at a reasonable cost for almost any model fro www.microtrim.com.

I wouldn't think so I did a countertop MW with trim kit.