EPDM Roof Cleaner or Not?

Use a mild soap dawn works good

I believe the reason your manual says that no maintenence is required for the roof membrane is that many folks tend to use harsh chemicals and treatments that tend to over time remove the chalked layers of the membrane causing it to thin.
A grime covered roof is one of the leading source of black streaks on the sidewalls and prolonged dirt buildup on the rooftop caulking shortens the lifespan of the caulk. I for one like to clean my roof regularly for these reasons plus it allows me to regularly inspect the caulk seams for cracking, leak sources, etc. I also use dawn dish soap and a soft brush. This is particularly important as I keep my rig parked under trees.
I believe roof conditioners are expensive and unnecessary.

Your manual is corect. There is no need to clean it other than it looks nice. EPDM is a roofing material originaly designed for low pitch/flat roofs, and was adopted by the RV industry. No cleaning required and excessive scrubbing or the use of products with citric acid or petrloium distilates can do more harm than good.
The only reason I can think of for making these products is that consumers want a clean roof and the products sell.

Water, bleach, Dawn in a yard sprayer. Sprays it on and 10 minutes later hose it off. If built up dust, ash, dirt does not come off use a SOFT bristled brush to remove. No conditioners.

As a retired roofing contractor, I can tell you that the white reflectivity of the EPDM or TPO roofs is not affected by being dirty, but I glad my 2003 lance has a white aluminum roof

Okay. Dawn it is.