The Department of Defense and police departments spend plenty of time and money on shooting. What we lack is will.
Motivated teenagers involved in organized competition and motivated to dry practice at home are better marksmen than most school-trained snipers, to say nothing of the general military population. Uncle Sam greatly outspends them but the kids have greater motivation to improve and actually do it.
You're touching on another problem, both in the military and in law enforcement communities: just because a shooter isn't required to surpass qualification standards doesn't mean that they're prevented from doing so. They're perfectly welcome to develop their skills further on their own time.
Anyone want to guess how often that happens?
Having done the DS Nitwit thing myself a few times, it was my observation that the range personnel were well familiarized with existing standards and courses of fire, and the manual was always available if there was a question. (There generally wasn't. It was all very simple.) We even went so far as to send recommendations back up the chain of command, which were diligently ignored by those who received them. When I enlisted in '96, that bullshit FBI flashlight technique was taught and everyone - from the instructors to the shooters - was fighting it tooth and nail. When I got out a decade later, it was still required to be taught, but was no longer required to be used for qualifying. I seem to recall hearing that it finally went away for good a few years ago.
This leads in to another point: government agencies, by and large, do not innovate. They are incredibly conservative and reactionary, much like large businesses (or indeed any organization over a certain size) seem to be. It's cultural in nature, but that culture evolved from experience. These organizations do things a certain way until that method no longer works, and only then is change possible. If the existing method is doing the job - however clunky or awkward it may be - forcing a change is nearly impossible, with the M16/5.56mm cartridge being a prime example of this. In spite of better alternatives, it works more or less adequately, and we're left with a 50-year-old rifle.
In some ways, this is actually a good thing. When such large, awkward organizations attempt to change a product without an external driving force, the result almost inevitably turns into a Mongolian goatfuck, and then we wind up with expensive turds like DDXXI, the ongoing F-35 debacle, Land Warrior, CVN-78, etc. So perhaps it's better if we don't push this.
I don't disagree with what you're saying. I just don't think that it's possible for a variety of reasons, both practical and ideological. But again, no one is preventing a concerned soldier or police officer from going off and getting gooder on their own. Most just don't seem to want to.