Maybe Kirk and Leighton were on the worst extended field trip ever?
The Star Trek: Federation book speculates that the colony was running out of food, and Kodos presumed there was no ship that could reach the colony in time to provide needed food, hence the executions as part of a lottery-induced rationing. Kodos failed to take into account the higher speed of the new Constitution
class ships, and the U.S.S. Enterprise
under April arrived in time that the executions were beyond unnecessary.
One would think that the married Kirks both being assigned to the Kelvin
was an oddity, and more often than not two Starfleet officers in the service together wouldn't be able to be together - similar to Geordi's parents in TNG. Maybe in the Prime Universe Winona Kirk retired from Starfleet after the Kelvin