Well to each his own, but if I bothered to slog up ptarmigan, yes, I would take skis and carry over. Once it is too steep to skin (pretty damn steep) it's too steep to snowshoe.
Rainier is for skiing. It's too much work, too much slogging not to have some boards with you. If the route is too steep to have skis on your pack, well, it's probably a chosscapade on the willis or somesuch and I wouldn't be there anyways.