How did Starfleet allow Earth to have only one appropriate ready to deploy ship in the neighborhood?
Around that time Starfleet was likely overhauling most of their ships or decommissioning older ones to be replaced. There may have been dozens of ships in the system, and Utopia Planetia or San Francisco Shipyards but they were in worse shape than the refit Enterprise. And even if there were others they likely wanted a Frontline ship with one of the most revered officers onboard than, say some rando under equipped Oberth with a B-team science crew of 70, or an outdated TOS-style last in line for refit.
Around that time Starfleet was likely overhauling most of their ships or decommissioning older ones to be replaced. There may have been dozens of ships in the system, and Utopia Planetia or San Francisco Shipyards but they were in worse shape than the refit Enterprise. And even if there were others they likely wanted a Frontline ship with one of the most revered officers onboard than, say some rando under equipped Oberth with a B-team science crew of 70, or an outdated TOS-style last in line for refit.