Its just a PITA. I hand wash and use spray detailer on them. My steps are, rinse, use a microfiber towel in the leftover soapy water, wringing out before re-dunking. Go around all 4, fill with clean water, rinse, repeat, rinse. Dry car off, dry wheels off (not the same MFT), spray tireshine/foam, detailer on exterior of the car, detail the rims.
I do it that way so I get the spittle off of the paint that the spray foam on the tires sometimes leaves. The double rinse gets the rims cleaner than just once and the second time is a lot faster. The detailer makes them shine a bit more, but it may help attract the brake dust faster--not sure.
They get dirty super fast, like around 3 days or so. It sucks, but they do look awesome while they're clean.