Parsons was for years a county sheriff of a rural county in Missouri (Polk County, current population ~30,000), so he was head of the Highway Patrol in the county. I suspect that as Governor he has strong relations with the Highway Patrol statewide and views them still as loyal and trustworthy to him, while he may view the more suitable branches of law enforcement (e.g., the cyber crimes division of the Department of Public Safety) as urban desk jockeys who may be less loyal and aligned with him personally, and therefore he'd rather send in his own troops for missions such as this.