I had a flood in the basement so the insurance company said they'd replace the carpet on the stairs. I don't want carpet, so will ask them either for treads, or to prep the staircase for painting. They probably will be contrary, leaving me to do most of the work. I think I want to paint a beige-toned faux marble on the treads, which I'd seal with several coats of water-based polyurethane. My question is how hard is upkeep in terms of showing dirt when considering painting treads versus having stained wood (faux marble will have many tones, not just one like one-color paint)? Yes I know the dirt will come with either but I don't want it to shout at my guests if I haven't cleaned it recently, nor do I want to be a slave to my stairs. TIA for any light you can shed on painted versus stained wood treads regarding upkeep.

This is my inspiration photo: