This theory falls down when you look at murders. They're down with all the others on that link, and they're highly unlikely to go unreported.
They're usually talking about large amounts of more "petty crimes" - because even in the murder capital of the US (currently St Louis) it is 64.54 per 100,000 residents. Just not that many overall and you probably won't actually know someone who was murdered, especially if you're more toward the richer parts of town.
But the other crimes are much more common and you will see them relatively often if they occur. I wonder what percentage of people have seen shoplifting or had a car broken into, etc.
It's more about the "feel" of the city than the "real", unfortunately.
Well, yes, that's the problem. It's a perception easily manipulated, by media breathlessly covering the latest incident, interest groups like police unions making false claims, etc. Americans have a wildly incorrect perception of what crime has done over the last ~50 years.
Put another way, the guy stealing your catalytic converter isn't doing it because he's afraid to kill you or burn your house down. He's doing it because he has every reasonable expectation of getting away with it and getting paid for it.
Catalytic converter thefts are up everywhere, though. Not just in liberal bastions, but in places like Arkansas and Mississippi, too.
Cops saying "if you just gave us more money and toys, we'd stop crime" is a claim that should come with significant evidence to accept.
I don't doubt it. I doubt the cops' unsupported claim that said difference is an effective deterrent against the crime.
We'd need some solid numbers on converter theft rates relative to the car-owning population. But even then the numbers wouldn't be comparable, so it'll always come down to my "common sense" versus yours. My common sense says that when cops see a crime in progress and walk away whistling, it encourages further crime... and also discourages the victim from bothering to report it.
In fact, it looks like murders in San Francisco have been in roughly that range since 2009 (https://www.macrotrends.net/cities/us/ca/san-francisco/murde...).
[1] https://www.sanfranciscopolice.org/stay-safe/crime-data/crim...