- each public school has the same budget per student. There is no "reduced education funding" for schools in district X vs district Y, or for any school, because the budget per student is equal. Each school's budget is public, and published on the web.

- favoring religious teaching: at least at the school my kids go to there's absolutely no religious teaching. I suspect this is the case for all the public schools in NYC

- nuanced policy difficulties? Not sure what you mean by this

Ok, now to answer your original question: why the fault of progressive left. As you see I skipped the word "extreme", as this is a loaded word; people who vote that way certainly do not perceive themselves as extreme.

At the recent mayoral primaries, the top candidates were the moderates Eric Adams and Kathryn Garcia (1st and 2nd place), and the progressive Maya Wiley (3rd place). As far as the education was concerned, the hot topic was the selective "specialized high schools" [1], where the admission is test-based, according to a state law passed about 50 years ago. The current mayor (Bill de Blasio, progressive) has worked tirelessly for the last 4 years or so to lobby the State legislature to get the law repealed. The progressive candidate, Maya Wiley, promised to work towards the same goal. Here's the relevant extract from her platform [2]

>> To remove barriers that separate and label children, we will: [...] Eliminate discriminatory admissions “screens.”

In other words, kill the specialized high schools program.

Eric Adams (the winner, moderate) promised to keep the program as it currently is.

In case you wonder what the admission entrance exam is like, it's just two separate tests, one for ELA and one for math. Both tests are fairly challenging. The progressives think that these tests (and especially the math one) are discriminatory in nature.

Here's a sample math question [3, p.78] "In Centerville, 45% of the population is female, and 60% of the population commutes to work daily. Of the total Centerville population, 21% are females who commute to work daily. What percentage of the total Centerville population are males who do not commute to work daily?"

[1] https://en.wikipedia.org/wiki/Specialized_high_schools_in_Ne...

[2] https://www.mayawileyformayor.com/maya-wileys-plan-for-creat...

[3] https://cdn-blob-prd.azureedge.net/prd-pws/docs/default-sour...