Yes it would become thinner, but a good detailer would do their best to take care and not to cut too much, abuse and put your paintwork in jeopardy. Also, by the word 'thinner', in the right hands, it's not as dangerous as you think. I would say, roughly, you can compound (or cut) the paint 2 or 3 times and still have a healthy coat of clear coat on the paint. I had sanded my own waja once, compounded twice and polish a couple of more times and, so far, the paint is still doing fine.
Just make sure the place you're sending knows what they're doing. About the price....not too sure. Need to as the pro leh....hehehe.....