It sounds like you're more likely to be shot by a member of a police SWAT team than a regular patrolman but perhaps police work isn't supposed to be about shooting people very often.
If you re-read your copy of "Shooting to Live" by Fairbairn and Sykes, you will notice they had their own theory of firearms training and ordinary target shooting, as they saw it, detracted from one's gunfighting skills. But then again, they weren't so much concerned with SWAT teams. Others, not surprisingly, have a different view of the matter, and some even recommend competitions. While ordinary ranges are poor simulations of gunfight senarios, competitive shooting at least provides pressure.
Perhaps one reason policemen do so poorly in actual shootouts, hit ratio-wise, is the simple fact that hardly anyone trains under any conditions approaching a real gunfight.
Shoot low, sheriff. They're riding Shetlands!
Underneath the starry flag, civilize 'em with a Krag,
and return us to our own beloved homes!
Buy War Bonds.