I agree that it’s absolutely ridiculous. Even when I was a teenager and saw the movie for the first time, I remember thinking to myself that it was insane to send a ship captain in the military to rendezvous with the head of state of your greatest enemy, who you are about to negotiate a historic and unprecedented peace with.
Even if you send Kirk on that mission because of his proven military prowess, there is no way you don’t staff the Enterprise with an entire brigade of Federation diplomatic personnel, ambassadors and specialists. In TOS, for infinitely less sensitive situations, they always had a Federation diplomat there to run that part of the mission.
It’s one of the many reasons I don’t love TUC as much as most people do. The foundational premise that they’d send Kirk out there alone with no diplomatic back-up or oversight is completely inane.
Even the script seems to acknowledge this as being under-baked stupidity, as Kirk himself protests that “a full ambassador would be better equipped…”