My Dad was in the Maricopa County Sheriff's Mounted Posse during the 1960's and early 1970's, and each deputy (regular or posse) had to furnish his own weapon. The requirements were: Colt or S&W revolver, 3 1/2" to 5" barrel, .38 Special minimum caliber, any higher caliber recommended, subject to qualifying with the specific weapon. The most popular were .357 magnums, with a few .41 and .44 magnums also carried. Most carried full magnum ammunition, but every deputy was required to carry six .38 Spl rounds in addition to ammunition for his own weapon, in case a fellow officer (most probably armed with a .357 or .38) ran out of ammo in an extended gun fight! Dad carried a 4" Python (1st year of the 4" Python manufacture) loaded with 158 grain jacketed soft points (used both Winchester and Remington). He also had at least one box of 158 grain armor piercing .357 magnum (Winchester, IIRC) that was issued for road block duty. I may still have that box of ammo around, I'll have to look for it. Kind of neat, a conical end projectile, FMJ.
The 125 grain HP loads didn't come out until the early or mid-1970s, and became the whiz-bang load generally preferred by LE (for those that could carry magnums); however, the .357 had a long and succesful LE career with the heavier 158 grain SJSP loads - pretty much a guaranteed stopper!