I once asked my Niece who used to teach in public schools, if unions had any say so about curriculum, she said no, they were about pension, pay and other issues like that. Unions have influence in job protection and no, it's not impossible to fire a teacher except there are probably some places where this has occurred, but it's not the norm.
Your comments are dead on with one exception. Teacher tenure, which everyone bitches about but does not understand, is the problem.
Firing a teacher is easy if they are doing a poor job. The problem is that what most people see as doing a poor job is exactly the kind of teacher that school administrators want these days.
Let me explain how tenure is a double-edged sword.
In my first job, I taught for 8 and 1/2 years and attained tenure status. I then became an administrator and my boss did not like the fact that I was a threat to her job, so she did not renew my contract and hired her close friend in my place. I was already in training for a principal position with the school district at the time.
In my next job, they were having fewer students the next year and I was the building union rep. Gone. Ex-military officer/administrator qualified in a Department of Defense school and union rep. You do the math.
I went to work in a public middle school and the district budget was slashed. Gone. last hired, first let go.
Moved to an inner city all-boys middle school which was ranked the worst in the state. Taught there three years. The last year, students were physically assaulting each other in my classroom, and when I stopped them, I got an ass-chewing from the principal. Gone. I was leaving anyway.
Spent 1/2 a year replacing a teacher fired for sexual misconduct with a student. Outstanding evaluation, but since I only taught a half-year, I was not eligible for rehire in that position.
Took another job at a school closer to home, and spent 4 years there. I loved every minute of it and received outstanding evaluations. Up for tenure on day one of year 5, so they let me go after 4 years, no reason required, so I was up the creek without a paddle. Gone.
Last year, any teacher without tenure is automatically not renewed. They found someone cheaper. Gone.
This year, districts looked at my series of non-renewals and justified that as a reason not to hire me. Took a long term substitute position. I taught first 25 days of school for reduced pay. When they had to pay me my regular salary. I had to turn in my ID badge and keys. No reason was given. Principal banned me from working at the school despite my having done nothing wrong. He didn't want students asking questions as to why I suddenly left.
That's the side of tenure that none of the public gets to see. It sucks if you are on the wrong side of the barrier.