The teachers that I know work tirelessly, don't make very much money, and do literally everything they can to help students. This is doubly true during the past year when they've had to re work plans so that they work over zoom or in person.
I think perhaps the point of friction is that all of this is true and the city can't afford to pay them more, so they get other concessions.
I fundamentally disagree with your claim about lack of innovation - in a public high school 15 years ago your story doesn't ring true, much less seeing my friends who are teachers talking about lesson plans today.
I mean, have you seen the American Education system? Millions of people thought Betsy Davos was a good idea. MILLIONS. The DOE under her tenure was basically a full on assault against public education in favor of charters/private schools. I've had hours-long, in-person arguments with people who are CONVINCED teachers have the easiest jobs on the planet and we pay them too much.
Not to mention many HN commenters in general tend to strong pro-management stance which pushes them anti-union in general.
That and hyperlocal funding.
We can't like society as a whole fall part and expect schools to keep on performing well.
A couple of years ago there was endless complaints about new ways to teach math.
There are anecdotes to support the point of view they are bad, and anecdotes to support that they are good.
The source of funding does not seem to be the problem. The quantity of funding, definitely.
I've personally known three people who got elected to their local school boards without any endorsements at all. They all had big families, literally just a lot of people knocking on doors evening after evening, no prior political experience even.