I would say that the amount of wax protectionyou get from the car wash is minimal at best.
I tried the new Rain-x wash and wax product recently to do the roof area, as it so hard to get to, but the jury is still out for me on how well it will work.
The liquid hand applied wax, or a good paste non abrasive wax are the only real protection you can have.
The good thing is that unless you live in very strong sun areas or somewhere near the coast salt air, you should only have top wax with a good product maybe twice a year. I use the liquid wax more frequently as it is not as hard as the paste.