I am not now, nor have I ever been, a Police pilot.
I have, however, flown with Police pilots on operational sorties, and am entirely familiar with the very demanding nature of the job.
There may be circumstances where the use of a light, single piston helicopter is appropriate for police/law enforcement support, but I would suggest that such circumstances would be unusual.
I would further suggest that a professional pilot is worth his salary in this environment, and that someone with PPL levels of skill and experience would be unlikely to be able to undertake the role effectively or safely.
It would be cheaper for Southwest to employ PPLs as pilots, but no-one in their right mind would suggest that they should do so. Flying an airliner is beyond the competence of a PPL. The same holds true of police aviation - the job demands a professional pilot. And yes, you have to pay for that. Pay peanuts, get monkeys.
I would always prioritise operational effectiveness and safety (both for the crew and for the public on the ground) over minimising cost to the taxpayer.
I would suggest that US attitudes to taxation and central government may be mitigating against giving airborne law enforcement the tools that it needs to do the job, and may be forcing some operators into sub-optimal practises and procedures, in a misguided attempt to pare spending to the bone.