Would Kirk's age fit battleship command?

Would a thirty-five-year-old officer such as Captain Kirk command a battleship?

Normally no, which supports treating the Enterprise as a long-range cruiser rather than a battleship.

A captain of about thirty-five would not normally receive battleship command. That age fits the Enterprise more readily as a cruiser sent on exploration than as the fleet's principal battle asset. Size alone does not decide the classification because endurance and long-range service can make a cruiser very large. Mission, command responsibility, and career experience matter more than hull dimensions here.