I had a set of wheels professionally polished, powdercoated and cleared a couple of years ago. The bare aluminum under the clearcoat oxidizes and gives a cloudy appearance to the clearcoat film. A paint cleaner will clean some of the oxidation from the surface, but will not remove completely the metallic oxidation that is in (yes, suspended inside) the wheel's clearcoat film.
My technician recommended three polishes that can effectively remove the cloudy oxidation residue that develops occasionally on the surface without stripping the clear (BM, Flitz, Simachrome). I double checked the wording on the labels, and Blue Magic states that it is formulated to clean oxidation from factory coated wheels. Flitz states that it is effective on polished aluminum, fiberglass, vinyl, plexiglass and a host of other materials. I will correct my previous statement, because Flitz did not specifically state clearcoat as a surface; However, it did state that it is a non-abrasive polish, and it has worked well as per my tech's recommendation.
I have used both Blue Magic and Flitz (flitz is a more active cleaner, while blue magic has a better polishing effect) with excellent results. I once tried a paint clearcoat cleaner on my newly clearcoated wheels when I first got them back (prior to that also on an older set of factory clearcoated machined faced wheels) from the shop, and the paint cleaner would not remove the oxides (via hand). For painted and cleared wheels, you may be able to use a paint cleaner with good results, bc the paint and clear provides a better insulator to the bare aluminum. In time, without care, even painted and cleared rims will show signs of oxidation (cloudy patches, white patches with prolonged abuse). The oxides (not a chemist, so bare with me) gets suspended into the clear, so you will need a product that can chemically react with the oxidated residue and clean it from the clear without abrasively cleaning or scouring the surface.
Anyway, sorry for the read and no disrespect intended.