Secondly, in the case of the USAF, with only 180 odd F-22s available globally, then surely the F-35 will have to undertake a considerable amount of air superiority tasking, no matter what it was primarily designed for?
Two comments back atcha:
1. The F-22 is not the only air superiority fighter in the US or NATO inventory. It is the only
stealth air superiority fighter, but there are several hundreds of non-stealth air superiority fighters (F-15s, Typhoons, Rafales, etc) in the various inventories.
2. I believe there is a significant difference between "focused on maintaining air superiority" and "undertake a considerable amount of air superiority tasking."