I'd go out on a limb and say that in general they are pretty bad for a car over the long run. Especially those with moving parts that touch the finish of the vehicle.
The ones that have some sort of contact with your paint turn me off right away. Kind of hard for me to believe there wouldn't be some stuff in the brushes/foam that I don't want rubbing on my paint.
It is often more than just the car wash machinery. At a popular one in our area, they do wipe downs on all vehicles after the wash. They are not using a clean towel for each car so they could be picking up residue dirt not removed during the primary machine and then wiping it off the vehicle and subsequent vehicles. I see some very expensive cars going through that place.
At the one that the company I used to work for took the company cars, they quite often didn't even wash the towels after using them. Just threw them in a dryer and used them again. At some time, they were no doubt washed, but it wasn't real often.
A Automatic car wash is better then no car wash at all. Some people simply wate until it rains to wash there cars. I know some .
Kind of my thought. The underbody wash will at least remove some of the sand/salt accumulation and although the chemicals in the touchless ones are probably tough on your LSP, they probably aren't any worse than the salt.
The touchless one in our area doesn't use recycled water and I will sometimes get just a plain wash, (no wax), then finish at home with S&W.
The touchless one I go to does
not remove enough of the dirt for me to want to dry it after using the wash cycle. The S&W does a good job removing the film the wash left.
As far as the LSP, I can usually manage to refresh it a few times during the winter so I feel pretty comfortable with the protection.