Only if it can be shown they are more accurate with that weapon and at least able to qualify as "sharpshooter" if not "expert" with their assigned duty handgun.
Most cops can not shoot well!!!
In LA they would have been able to end the action in minutes with a simple .30-30 deer rifle in lever action if they'd been able to make the head shot! Max effective range on the 5.56mm rd is 460 meters. I can just see dozens of "Kent State" scenarios when jittery cops start prayin' and sprayin' and they miss.
I'm just a little ol' civilian whose daddy taught her to shoot a .45 and a .30'06 deer rifle . . . I worked one summer for the police department, and I could out shoot every single one of the officers on the range except for one lieutenant who was also a sport shooter and gun collector.
I think you were on the thread where I mentioned a shootout between two officers of one of our local PDs and an armed robber . . . the officers had 9mm Glocks with a couple spare magazines and the best they could figure afterwards nearly 100 rounds were fired and NOBODY hit ANYTHING . . . not even the robbers car . . . although a dumpster at the edge of the parking lot sustained a couple of hits.
I think the problem is that to your average police officer the sidearm is just another tool, like a radio or a flashlight, and their competence is about what you would expect in that situation.
Giving them full auto is going to just encourage more "spray and pray" with predictable results.
They need to find the sport shooters and hunters in the PD, give them each a nice Remington 700 in .308 with a Leupold scope on top, and a couple hundred rounds for practice. When they are MOA accurate at 200 yards, they're ready. Shouldn't be too hard.