When it comes to recruiting and training new officers, every additional requirement you impose for a new recruit (age, experience, education, police record, etc) is going to decrease the size of the "pool" from which you recruit.
After all, you can't "draft" people into the police force, so in reality, you don't have a choice of a cross-section of the population from which to choose your officers: You have a choice of those people who (a) actually WANT to be cops in that city or state, (b) are physically, mentally, and morally qualified and (c) make it through the screening.
The tougher the screening, the fewer that are going to make it thorough and the less choosy you can be about who makes the cut.
Unfortunately I don't think there's an easy answer or a simple solution here. I foresee a "Ferguson Effect" on a very large scale looming in the future, though, especially in major cities. Expect the police to slow-roll their responses to calls and to spend a lot of time doing "paperwork" in the donut shop parking lot.

