Many of the coin-op car washes use some sort of high quality synthetic brushes that are quite soft. The bottom of those soap buckets also has a grit guard type object to trap dirt. It is not ideal, of course, to wash your beloved cars at the coin op, but if you must necessary wash your car at one of those places, you shouldn't worry too much about it.
Those soaps they use are not your typical consumer grade car wash soaps. No, many of those places use some very high quality industrial grade soaps that can really dissolve grime. They use powerful shampoos to prevent sludge and tar from sticking permanently onto the brush, and to make your life easier. Those soaps do in fact strip wax to a certain degree, but they are also rich in polymer to seal in the paint to repel dirt.
Coin-op car washes are operated by profit-driven business establishments. They want your business repeatedly, not just once, and in order to do so, they must provide some quality assurance with their equipment and material. Of course, I am speaking about competitive coin-op washes in populated cities where there are competitions.