Allergies in the house means as much carpet as possible is going to be banished. However all of the information I'm finding online suggests that most carpeted stairs are not particularly attractive underneath and that having hardwood installed is Not Cheap. Has anyone else dealt with this? Did you just leave the carpet on the stairs? Remove it and finish the stairs in some other way?

I've seen a couple of instances where the stairs were just sanded and then painted, but I'm not sure how that looks long term or how well it wears? There will be a large dog using the stairs so that is a concern.

(Right now I'm kind of thinking along the lines of hoping I can do something tolerable to the stairs with paint, and then using stair rods to fix washable carpet runners in place. So there's grip and protection from the carpet, but it can be thoroughly cleaned often enough to minimize allergy issues.)

I know a lot more people have allergies these days, though, so I figured I'd post and see if there's some genius solution I'm missing that won't cost as much as some of the prices I've seen for redoing the stair treads in hardwood.