I worked with a guy once that never washed his car. It was only a two-year-old car, but he wasn't from the US and believed car washing was a waste of time.

He lived in an apartment and parked outside, so the rain was his main wash. Spent most of the winter dirty. When the spring rains came, it looked pretty good.

He lived in the city, so it never got muddy from gravel. That he never vacuumed it was more of a problem. The carpets weren't so good.

if washing is left to the rain, there will be grey water stains when the water dries up.

This is a great idea, but others have already beat you to it. Check out this titanium oxide based paint and this other one promised for cars called Zyvere 2K Nanocoating. There are other ones too.