"Of course, the USAF has to say it can do CAS or they're undermining the Marines' claim that they can do any mission, in combat, right away."
I think that in service what may matter is the willingness of commanders to actually use the F-35 for CAS. Besides the fact that an A-10 was well designed for the task, the fact that it was not much favored for any OTHER task probably made it more available for CAS and more likely to be devoted to that. F-16's, F15Es, even "strategic" bombers can do CAS and sometimes are, but they are not routinely used that way. In a conflict where there are many tasks to do - CA, SEAD, interdiction, EW etc., where will the "multi-role" aircraft be used? CAS, perhaps. Where will the A-10 be used - CAS most assuredly - to the delight of ground troops and their commanders.
I would also posit that the survivability of a few high-cost assets could also affect an air commander's willingness to assign them to CAS.