I have not seen it done and I don't really think it would keep the staining down. Our last house we were talked into a white roof when we built. It only looked good for a few years. It was stained from just the air pollution in the rain and snow. Expecially where one downspout ran onto a lower roof.

I dont think it is always from a vent pipe. Several years ago, there was a brand new house built up the road from where we lived at the time. Within a year, the front of the roof (never could see the back), was badly stained. No vents on the front side of the roof, so couldnt possibly be from that. All light colored roof, show the same staining after a while, when they are asphalt shingles. I dont see that staining on darker roofs. Light roofs look old at 5 yrs, while darker ones still look pretty good at 15 yrs.

Most discoloration is a type of mold that forms due to humidity. It can be removed and preventatives applied to help reduce it growth. It appears to be staining from pipes but it is most likely because greater dampness is maintained in those areas and it keeps environment prime for this growth. Some Shingle companies are making shingles that resist this growth. Get a professional who can clean roof about every other year depending on your environment with non-clorox type cleaner being careful to not power wash off too much of actual grains from shingles. Check with manufacturer of your shingles to get their recommendations so you don’t void any warranty you might have.

Here is actual name of this algae which forms on roofs in humid environments.