But I don't want to use anything caustic...

Anyone recommend a product that truly cleans.but doesn't etch or otherwise damage..with a simple application, and a hose down???

I use brake clean

If they’re just straight up aluminum, I use fine steel wool and Mother’s aluminum polish.

Won't steel wool of any kind, scratch the wheels?

I haven't found any magic formula for cleaning wheels - just elbow grease. One tip is to be careful which brake pads you use. Metallic pad material rusts to wheels after it gets wet. Once that happens, I haven't found anything other than abrasives that will get it off.

Try a product that contains Oxalic Acid. 'Bar keepers Friend' is a very gentle abrasive product that has OA in it. Cleans stains on SS cookware like crazy (I use OA crystals in water on my cedar deck prior to the Cabot stain too. Works GREAT!). Do a small test spot. Check YouTube for using OA on aluminum.

Waxing your wheels will help, depending porosity and texture. If painted try ceramic coating them. These will help, but have never heard of a no elbow grease solution....

Mine cleaned up really nicely, no scratches. I used a slightly heavier gauge steel wool with the polish, then switched to fine (or maybe extra fine) and went over them again with the polish. I still need to clean up the inner black area, but won't use steel wool there!
before:
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after:
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nothing just cleans with a spray down, one has to use elbow grease, as there is always a film left. We have had good success with the Sonax wheel cleaner, which softens the brake dust and does not etch alloy wheels, and the a good brush, towel, and yes toothbrush (I always save ALL of my old toothbrushes!!
Like one of the previous comments, for the painted wheels, waxing really helps

Mothers, cotton rags and elbow grease. Howmuch elbow grease depends upon how often I polish the Fuch'ers. Twice a year takes about 5-10 mins a wheel. It's easier if I remove the wheels and stack them 2 high to avoid bending over.

Rather than steel wool, I recommend the gray ScotchBrite pads available at Lowes. These pads don't rust or stick like splinters in your fingers., I've used them for years in finishing my woodturnings

Mothers works well, I would not use a scotch brite pad or steel wool if you are just doing a clean and deoxidize you will scratch the metal and then you are in for a 6 sept process to get those deep scratches out.

For basic cleaning, including brake dust/film, P21S Wheel Cleaner has worked for me, especially for the insides. Hadn't thought of light steel wool/Scotch Brite and polish for finishing the outsides; nice tip.