I go for a drive when its raining, in the spring mostly, drive through lots of puddles to wash off the salt. When I do actually wash the car, I do make a point to scrub the tires and wheels a bit.
Before kids, and monotone plastic jellybean cars, I used to wash and wax the '81 Olds Omega Brougham pretty regularly, get that chrome trim shining! And I used to love giving the white sidewalls a light scrub with a sos pad to make them pop! Even in the early 2000's white walls were pretty much over. I might've even tried some tire dressing on it? I haven't used any since at least.