A carrier can only go as fast as the slowest escort vessel.
Not true...there were times we were unaccompanied, or if we were, the escorts were nowhere in sight. It did happen. I don’t know if steaming doctrine in the Seventies was that much different than it is today, but I do recall it was not uncommon to not see another vessel anywhere out to the horizon. Of course, they didn’t have Aegis class missile ships back then, so maybe it was different.