Dog Friendly Stairs question

Hey all! Hoping to pick your collective home improvements brains-wisdom. At our house we have carpeting going up the stairs and in the upstairs rooms. The carpet was more than a little bit dead when we moved in, but it has moved past that into downright disgusting. The plan was always to get rid of it, but it needs to go soon. My concern is the stairs. They look to be in pretty good shape under the carpet, and I was hoping to get away with just painting them, but that's not going to be too good for big dogs going up and down and Little Dog, though she can manage them, does not like slippy stairs. I'd like to get away entirely from carpets if possible (Akitas have to be the grand high champions of the dog world for shedding) but I want to put something down that will keep their feet from skidding. I was thinking about rubber tiles, maybe? Does anyone have any experience with this sort of thing?

Functionality is further up on the priority list than fashion. I don't think we're ever going to be listed in Britain's Classiest Homes.

A lot of the issues are with the depth and angle of the stairs.