> If SF politics is really controlled by a wealthy cabal then why have they allowed the situation to deteriorate so much?

Because they can't influence supervisor elections or school board elections as well as they can elections for mayor. The reason why San Francisco mayors are always re-elected is because they're very middle of the road in terms of politics and risk tolerance. Activist policies are usually the product of the Board of Supervisors, the school board, the district attorney, or public initiative, all of which are completely independent of the mayor's office. Sometimes the mayor's office will try to head off policies by offering watered-downed versions as an alternative. This doesn't always work, but it does contribute to the sense that they share some of the more radical policy preferences.

If you don't believe that the mayor's office has been significantly more conservative than the other political centers of San Francisco, just look at the police department. However dysfunctional you think the police department, it's not because the mayor's office has ever appointed a far left, defund-the-police police chief that seemingly every liberal has been demanding for decades. Police chiefs are appointed by the mayor the same way the monied elite choose a mayor--someone who is middle of the road, will keep their head down, and keep things moving along as best they can amidst the fracas. And as you would expect, their performance always falls short because their job isn't to succeed, but to avoid failure.

In general the mayor's office is expected by the old money elite (and increasingly some of the new money elite, like Benioff) to be the caretaker of a city with often times very extreme and contradictory policy demands. They're expected to avoid controversy, blunt the extremists, negotiate (quietly!) among various interests (e.g. unions), and pick up the pieces when things fail.

> The wealthy people who control NYC politics seem less tolerant of such issues.

Maybe. But I tend to think that a more important factor is that NYC still has a larger working class. The upper middle class, which increasingly dominates San Francisco politically, is disconnected from the city. Their politics come from social media and national narratives. They're more focused on avoiding feeling guilty about drug addicts and the homeless than on actual results. That's why the policies keep getting pushed further and further left (far beyond what was ever demanded 10 years earlier) despite the lack of results.

The thing about the rich elite, especially old money, is that in many ways they're far more grounded than the middle classes, especially modern middle classes. If you own buildings or businesses, local politics matters immensely to you. No matter how conservative or liberal you are, what matters above all else is consistency and avoiding surprises. Consistency and security is critical because you're immobile.
The same is true for the working classes. No matter how pissed you are at economic inequality, the last thing you need is the ground constantly shifting underneath your feet. Similar to old money, consistency and security is critical because you're immobile.

San Francisco has too few of the latter kinds of people. At the end of an election cycle, its votes that matter, not dollars. The result is that moderates, which are still quite powerful, are always playing defense rather than offense.