The answer to why people wouldn't accept your proposal is simple: that is
part of the job that
we pay the police to do, and
they aren't paying
us to do that part of
their job.
You keep falling back to the excuse 'well, the police won't do their job'. If that's the case, that's the root cause of the lack of enforcement, and we need to address it. Who knows what other crimes they won't feel like investigating tomorrow? Domestic violence? Murder? Obviously we can't leave such discretion in their hands, rather than the hands of the people.
The excuses about police workload always inspire skepticism given their petulant tantrums and refusals to do their job in retaliation for being criticized for their wrongdoing.
Honestly, though, I'm just not convinced they're using the available person hours and budget in the most optimal way to achieve what the people want. If the police feel like they truly do need more people to do their job, however: like I said, they can submit themselves to civilian review to determine if they're meeting enough civilian goals to justify increased budget.