So in order to prove that the M-5 can withstand the combined force of four starships, they'd choose the task force commander to be a member of the administrative branch?!?
I'd think to prove how well the M-5 were able to handle an overwhelming attack force, Starfleet would have chosen a starship commander with sufficient experience, hence Wesley.
For all we know Lexington might be the flagship of Starfleet (implied by the unique, taller command chair) and therefore its personnel and commanding officer (Wesley) wears the starburst / flower insignia of Starfleet.
Bob
Kirk was also part of the administrative branch when he was Starfleet Chief of Operations. Just because one is currently part of the administrative branch doesn't mean they lack starship experience.