To add further to both WEBF and Frost's good posts, it's worth reminding folk that F-35B is not there to protect the fleet or the Carrier. Sure, if nothing else can provide AD then it will conduct DCA as a priority; in most circumstances it will be conducting strike, AI, CAS & ISR at range, and probably as part of a package.
Yes, you have to protect to project, but the protect function will be more logically covered by other fleet assets.