Troopers were historically neither police nor mere enlisted soldiers as they are colloquially called in the United States. They were soldiers in cavalry regiments. The word comes from the French troupier.
Troopers William Lawrence Sr Omnibit 11-29-18
Right. The word was transferred to police, because often those units that carried out police duties were mounted.
On a related note, “troop” is a collective noun; it’s incorrect to refer to a single soldier as “a troop”, though the geniuses produced by journalism schools over the past 30 years didn’t learn that distinction.
Now there are super troopers.