Although in both TMP and GEN, it makes no sense that there's only one ship available that close to Earth, the capital of the whole darn Federation.
Agreed. The in-universe explanation from David R. George's Crucible
series is that Admiral Nogura ignored Kirk's advice to delay the deep-space missions of several vessels because the latter was concerned about Romulan and Klingon incursions into Federation space. When V'Ger showed up a few weeks later, Nogura conceded that had he listened to Kirk, more ships could have intercepted V'Ger before the Enterprise
would have been needed, this avoiding the transporter and wormhole accidents that plagued the start of the mission.
A lot of this was actually addressed in earlier drafts of TMP, but was lost in the rewrites.
The Phase II television version of the script ('In Thy Image') has got explanations for most of TMP's plot holes, but the movie version cut out a lot of the exposition scenes contained in the TV version. Among them was an extensive scene where Kirk is briefed by Admiral Nogura, where it is specified that the fleet is close to Earth but is just slightly too far away to arrive in time (V'ger is going to get to them in 8.6 days, but the nearest other heavy
cruiser is nine days away). There IS also one other ship close enough to intercept V'Ger, the USS Aswan, but Kirk says she's a "light cruiser" with "less than half" the weapons and defence systems of the Klingons that V'Ger has already licked. The Enterprise is the only ship available with the technology to maybe
take on the intruder, which is why she gets pressed into service (and Kirk, against his better judgement in this draft, accepts command of her and rushes to try and pull together a crew with enough experience to take out as quickly as possible).