Fine Enterprise is the only ship in the sector--why the Enterprise is hanging around on a training cruise in a sector that has both a top secret research lab and Kirk's old girlfriend, who knows, but it is. Starfleet should have figured out something was up and sent out an extra ship or two to back up the Enterprise. "Could be nothing, garbled communications"...from your top secret research lab that's building a super torpedo that reformats planets. I think that's worth sending a cruiser or two to back up the outdated training ship full of cadets.
Actually, Regula-1 was a civilian
laboratory, and there was nothing "top secret" about it. The work they were doing there was a secret, but only because Carol Marcus didn't tell anyone but Starfleet what they were up to (in a request for funding) and Starfleet didn't go blabbing it to everyone willy-nilly.
It would be like getting an angry phone from call an antarctic research base about somebody messing around with their polywell experiment; the commander who gets the job of investigating it winds up using a google search to figure out what a "polywell" actually is.
Kirk defies all common sense, even after a junior officer tells him they should raise shields; to top it off Spock calls her down on it. The Enterprise crippled, a lot of the TRAINEE crew wounded, power failing, Kirk decides to continue on to Regula instead--oh I don't know--hauling ass to a starbase or getting out of jamming range and getting a squadron chasing down Khan.
That's his style, dude. He did the same thing against Nero. And it worked -- both times.