So what is about the mom and pop washes that makes you think it will scratch and swirl a coating but not the clear coat? Coatings are just like super durable coat of wax. Both a Prosumer coating and regular sealant of wax product are basically sacrificial layers that protect the paint underneath. If it's marring a coating, I guarantee it will be marring clear coat. And a "good Marine wax" wont stop that from happening, a coating like CSL or Cquartz is much harder and more durable then any wax product.
There's nothing special about washing a car with a coating. I use the same two buckets I always have with meguiar's Gold class car shampoo from Costco for my weekly or bi-weekly maintenance washes. The only thing different is that maybe once or twice a year it's a good idea to use something like CarPro Reset to help restore your coating and or use something like wetcoat or reload to boost the protection a bit. Which is really much easier and less time consuming then waxing your car every 2 months or so. Why would you spend more time and be careful to wash a coated car then you would a non coated car? I'm sorry, I'm just not understanding the logic here at all. The whole point of coatings is that they are easier to car for, aid in preventing swirls and scratches, makes washes easier and only need to applied every 3-5 years in stead of every couple of months like wax.
If you watch some examples of good coatings and sealants, you will find that certain types and brands are very slick to the touch. So slick in fact that a microfiber towel will slide off of any surface that is not level like the hood. The SIO2 products do this very well. Another positive of such a slick surface is that a lot of dirt and contamination comes right off with a rinse down. A wax generally does not have this effect.
There are a lot of good sealants on the market that can be applied by the owner without special tools. Gyeon has been mentioned and they are good. There are several brands out there. Autogeek is a great source of info as is Esoteric car care with their YouTube channel.
Don’t forget the interior as well. In my CX5 I used Gyeon Leather Coat on the seats and in the soft panels of the doors. Rain just beads and falls off. The surface remains smooth. The finish is a low satin which is ideal for interiors.