Well, don't know how it is in the States, at least in my employing agency and over here, we can't use our own ranges at will. We qualify four times a year, usually shooting 25-50 rds, depending what kind of drills are to be carried out.
I have myself asked if I could use the range on my own, purchasing my own ammo. Answer, NO. The range is to be used under the direct supervision of a supervisory officer. Reason, they don't wanna run the risk of any idiot shooting his own foot. My own supervisors agree that it's quite unfair, and that instead of assuming that we are a bunch of idiots who need to be babysitted at the range, it should be the other way around. Assume we're professional enough and take action if someone is not. But rules are rules and that's the way it is. Solution?. Join a club and shoot as much as you feel like, and that's what I do.
Among my coworkers, and we are more or less 40 guys in my unit, it's just three of us who shoot handguns regularly. Some others hunt with rifles and shotguns, but the vast majority only shoots during the qualification drills, and that's it. It's true that the average cop is not a shooter "per se", and this, I'm afraid, is this way all around the globe.
However, let me make a point. There's a BIG difference between being a cop who is an average to good shooter, and having what it takes to be a SWAT. From my American cop friends, I know that the SWAT standards in the US are different because you have so many different agencies, different in size and manpower. Put it this way, it's not the same the LAPD SWAT (as far as I know they have a fine reputation) that the SWAT of a smaller department in a smaller rural community somewhere else. SWAT standards here are HIGH. Our guys are at top level. They undergo a 9 month course in which they are taught every thing you might imagine. They train them to operate in virtually ANY condition and environment. As far as I know, they get the usual shooting, CQC and hand-to-hand combat training and physical fitness, but they are also trained in parachuting, combat diving, boat boarding/assault, bomb defusing and even train with the army in arctic, desert and jungle stuff. The unit demands, and the course takes a very particular kind of person to go through all that successfully, and most applicants just don't make it.
One of the things I like training when I'm at my club's range is placing IPSC targets at different distances and practice double-taps and transitions between targets. It's about double-tapping every target and transition to the next as quickly as possible. I like to do this without using the sights, kind of two handed point-shooting. From this, I know I can hit a person sized target at a range of approx. 8 meters without using the sights, if I was under an attack so quick and aggressive that I needed to shoot as quickly as I could. In real life, however, there's the stress factor, but I try my best to be ready for it, whilst I pray that it never happens. I also practice different stances (favourite are modified isosceles, weaver and crouch) and shooting one handed/weak hand. Some other times we simulate being sitting inside a car, getting out, taking cover and returning fire, shooting from cover, providing suppression fire for a buddy who's running for cover, etc...
That statement of "train as you fight, fight as you train" is a very wise one.