Are you seriously suggesting that the F-35's role is to provide CAPs for a task force?
Short legs, no AAR, limited AEW and low aircraft numbers make an uncomfortable 24 hour defensive capability for a UK TF. The USN can do it but our capability falls considerably short of the mark.
The UK's vision is for carrier-enabled strike - aka floating airfield. It requires other ships to provide defence for it. Using an F-35 to provide defence against small boats is equally questionable.