I can offer a few observations and anecdotes.
I am, for some reason, one of the few "civilians" invited to a monthly shoot directed at law enforcers and conducted under IDPA procedures. We get FBI, military, city, county, private security, and even a couple of mercenaries headed to Points East. It is the rare LE who can keep up with an IDPA Expert or even Sharpshooter. As our host, lawyer for the police union and the range operator, says to the LE, "These guys may not know much about investigating crimes, but they can SHOOT."
Of course we are all self selected, not average. And the cops are showing significant improvement in marksmanship because they are motivated to get out and work on it.
A deputy here once asked the sheriff if he could count an IPSC match as training time. The boss said yes, he could take two hours of paid time to shoot a scheduled match. So we would run him through the stages first so he could get done in two hours on the clock. He talked it up at the department but nobody else thought it worth his time. Too bad, he is now on city SWAT and can get a gun out of a Level III holster faster than I thought possible. But he worked at it.
A town PD dispatcher asked if he could use the department range to hold IDPA matches. The chief oked it. Some of the LE hung around to watch us in action the first time out. The second time out a number of them participated, even providing a patrol car with lights running to liven up an evening shoot. The next time or two, we got almost the whole department, everybody not actually on duty at the time. Shooting skills ran from quite good to scary bad. But not THAT good. One of our guy's 13 year old daughter beat the whole department. Part of that was on equipment, the better shooters in the department did great until their guns ran dry. Those horizontal magazine pouches with long Velcro flaps are made for security and comfort in the patrol car or swivel chair, not a fast reload and digging ammo out of them put them way down in elapsed time.
For some reason we didn't get invited back after that.
I once had a course at M.I.S.S. Besides me and an airline pilot, the rest of the class was military or LE. Or both, we had an MP who was using his leave to work on his shooting. He hoped to get on the Border Patrol upon discharge from the Army.
I learned that the sidearm is definitely secondary for the military, those troops needed the work. I also learned that New Orleans PD supports marksmanship. One NOPD was an excellent shot and the other was working hard to improve. They do have a crime rate in NO, I understand; even before Katrina.