Some dealers do it all the time, and most customers like that. My Lexus dealer has a "touchless" car wash and all cars in for service get washed at "no charge." I think many dealers of more expensive cars do this, but I'm not sure which ones do and which ones do not. All Lexus dealers do this as a mandatory policy; at Mazda, my guess is that it's an option with the dealership.
I, of course, don't want anybody else or any machine washing my car, so I have a page printed up that says "Please do not wash this car today." (I find that the "please" gets a better response than "or buy me a new one," which is hardly an accurate measure of damages anyway). I put this on the dash of the car when I go in for service, because a mention of this request to the service rep will sometimes get lost, and the car gets washed anyway.
On the way home, I put the page in the glove box where it waits for the next visit.