Some people prefers hand car wash because the person washing the car can pay more attention to the spots which needs more attention. Automatic car washes tend to be good for general washing, it does not have 'eyes' to see which parts need more work done. Of course even if you have an automatic car wash, it does not mean that you cannot offer hand car wash. I supposed you can provide the automatic car wash then get your guys to inspect what parts need more work and have them manually do the cleaning for those spots.
If you live in a northern country where there is lots of salt in the winter than definately as people with nice cars who can also afford the price of a wash 6-8$US to keep the salt from eating it.
I know that when winter was for the most part over where I live, there were huge lines in the carwashe lanes on the first warm day. Generally, about a dollar or two is spent on car washes that make the driver clean it. (self-clean washes). Since it is only using a bit of soap and a lot of water, I would say there is a fair profit involved. Don't think it'd bring crazy profits...but something stable most likely.
Probably depending on the soap.. honestly I wouldn't invest in such business, maybe a manual one from time to time