Any criminals with more than a single brain cell already know what cop response times are in their area. In the 60s-90s everybody had police scanners and cops talked over open radio about their locations and calls but crime still dropped massively in that time.
We already live in the safest time in the last few hundred years atleast, if not of all human history, all these fears about rampant crime are unfounded. And most crimes are committed by people you already know. Hell the biggest source of theft in the US, which dwarfs all other forms of theft combined, is employer wage theft. The cops deserve no trust because they have spent the last 6+ decades doing everything possible to militarize and become more draconian while extorting the poorest of society for fines and funding. Civil forfeiture laws are still abused on the daily and the entire US population knows it. Trust is earned, not given, and US cops and courts have done everything possible to destroy any trust between them and average citizens.
Maybe if I could trust that being executed on the side of a road by a cop in full view of the public and on camera would result in them going to jail people might support them having a bit of leeway, but they have repeatedly destroyed that notion. Cops are a far bigger threat to me than any petty criminals, most criminals were driven to crime through desperation so I can atleast sympathize with some of them. I have yet to meet a cop that wasn't a complete and utter asshole looking for any excuse to arrest or harass me or others around me.