It actually definitely would impact profits, because it allows you to switch your skins to suit your current champion roster, instead of having new champions you love incentivize you to purchase new skins.
Currently if I've been playing a ton of Tristana (like I usually do) and buy a Tristana skin I love, it's mine forever. If I later go a period of several months without playing Tristana, I may be tempted to pick up a skin for my current champion-du-jour (which I have). Under your system Riot could easily have lost out on the money they got from me buying Arcade Miss Fortune, as I could simply have used IP to purchase a refund for a Tristana skin, then bought the MF skin with that same RP. Once I'm done with my MF kick, I'd just IP-up and repurchase my Tristana skin.