But see, even with my idea you can have F9 by itself. Nothing will change for people who only want to see one (except that pressing F10 won't switch, it will add. You would then press F10 again to go back to only tires, instead of pressing F9 to switch back to tires).
I really don't think there's any drawbacks for anyone (except Scawen who has to code it). The script to rotate F keys would be broken most likely, but I'm sure someone could code up a new version that takes this into account.
Configurable F keys would probably be the best idea overall though.