There is no way in hell you power wash an asphalt shingled roof. You will ruin the shingles and possible squirt water under. Shingles are made to cover the roof from water at all angles, they are designed to cover the roof from water generally shooting down.
I had a roof that had a few trees over it. It too got moss, some algae. The best way to deal with the moss is to go up on the roof (summer is best) the day after it rains on a hot day. The moss will still have water it is retaining. Bring a small semi-stiff broom with you and literally nudge/pop the piece of moss out with the broom. They pop out generally really easy.
After you do that hit the roof with a leaf blower and get all of the debris off. Best to blower with the shingles not under them. You really want to get the loose dirt the moss has collect as you don't want anything lifting the shingles up.
For the algae there are numerous products that you just spray on - always good to do it about 1-2 days before a storm. These products require no washing after. I also would concentrate on just the problem areas not the whole roof.
On my old house this was just a yearly routine that I did every June. A small amount of moss will probably not hurt your roof but as it grows it gets big enough to pull up the shingles and wicks water under. Also I have had shingles deform and get brittle after detached (thinking about houses I flipped). I have had to repair/replace a few roofs in my life that probably could have made it another 5-10 years if maintained.
Summary: Nobody should be scrubbing or power washing your roof. A small broom and a leaf blower is all that I have ever used to clean off a roof and I don't use the broom to sweep, I used it to pop off anything stuck to the roof. An asphalt shingle roof that is getting moss means it is shaded or partially shaded. Maintaining it well without overdoing it means that thing could literally last forever. These shingles fail due to long sun exposure, too much wind/rain, and the wear layer coming off (wind, branches, cleaning...). The house I mentioned had 15 year rated asphalt shingles that were 40 years old with no leaks, cracking or tears... And only replaced them to sell the house.