Because if the DA says he won't prosecute certain crimes, why would the police bother to arrest someone that will be released on no cash bail. Why would they risk themselves or being in a situation where they need to use force and come under public scrutiny?
In many of these cities, these DAs are propped up with insane campeign funds, get elected, and refuse to charge, or push for no bail, so someone gets arrested for a felony, they end up back on the street the next day. Just read some of the cases where some people are arrested over and over and keep reoffending before their trial date.
The "certain crimes" that the DA said he would not prosecute are, in his words, "Crimes such as public camping, offering or soliciting sex, public urination, blocking a sidewalk, etc.".
It's a bit of a leap from there to conclude that attempted murder would not be prosecuted.
It's a different DA, but the current Manhattan DA (who appears to be from the same school of thought as the one under discussion), upon taking office in January 2022, issued a written policy memorandum which stated that his office will stop prosecuting, among other things, trespass, jumping the turnstiles, and driving without a license or on a suspended license; and further downgraded burglaries and drug cases, in some cases from what the text of the law classifies as a felony down to a misdemeanor.
Does it say anywhere on that memo that attempted murder would not be prosecuted? Of course not. Do these policies generally increase the feeling of lawlessness in the jurisdiction? Yes. Might that precipitate higher degrees of lawlessness? You be the judge.
You're making a "broken windows" argument here, which may or may not be true. But what I was discussing was a different question: Whether the DAs in question classified stabbing / attempted murder among those crimes not to be prosecuted. And I have not seen any evidence that they have.
In many of these cities, these DAs are propped up with insane campeign funds, get elected, and refuse to charge, or push for no bail, so someone gets arrested for a felony, they end up back on the street the next day. Just read some of the cases where some people are arrested over and over and keep reoffending before their trial date.