Hoping to get a reasonably clear answer on this. Should wash and drying media be cleaned after every wash? Here is what I currently do for traditional washes using a two bucket method

Wash mitts (microfiber and wool mitts) are rinsed thoroughly and dried. They go in the washing machine periodically, usually after 3 washes.

Towels (I use WW and a Griots PFM towel) ,assuming they picked up no dirt, are hung up to air dry and are machine washed periodically, every third wash or so.

For rinseless washes, I machine wash the mitts every time since this method keeps the dirt on the mitt (and I use several when washing a car this way). I usually hang the towel out to dry.