Worth consideration is that Spock Prime was already back at Starfleet Command when the decision to leave Kirk in command of the Enterprise was made. Imagine a (obviously actually longer) conversation that goes something like this:
Spock Prime, speaking to the Federation President and the Admiralty: "So, in conclusion, gentlebeings, we can go ahead and act to preempt all of the threats (V'Ger, Khan, the Whalesong Probe, the parasites planning to take over Starfleet, the Borg, etc, etc) that I have just outlined for you. Oh, and I'm sure you'll agree that the Enterprise command crew as I knew them needs to be kept together with Kirk in command, to sharpshoot any other problems that may arise or that can't be preempted."
And if you think about it, this actually provides a REASON that the Enterprise may be "the only ship available", at least in this continuity: Starfleet is sending them on purpose.