Why didn't other ships pursue the USS Enterprise?
It's a somewhat confusing issue. If we assume Genesis is relatively close to Earth (so that Kirk could wander to the general region during his birthday joyride), and merely in a generally neglected rather than horribly distant corner of the UFP, then when one starship fails, there might not be time to scramble another until Kirk was already there. And diverting random ships from everywhere in the Federation to block Kirk's access to a place nobody should visit would be counterproductive, as Starfleet would end up with half a dozen unauthorized ships at Genesis instead of just one!
Then again, if Genesis indeed is fairly close to Earth (that is, close to the place where Khan was marooned, that in turn probably being close to the place where he was found, that in turn necessarily being fairly close to Earth), Starfleet should have a great number of ships to choose from. After all, while many ships explore the unknown, it still makes sense to have plenty of them near the UFP core worlds as well, if for no other reason then because that's where they'd be the densest when moving out and returning from the frontier. They then could divert a trusted ship and skipper to intercept Kirk. They'd know the Grissom
wouldn't be up to the job, even if JT Esteban was...