My wife is an administrator at a public school, and as such I know a lot of teachers.

I've yet to meet any that say the limiting factor on their decisions is government interference.

I'd say the thing I hear most with regards to limiting their ability to teach/choose curriculum is how litigious American society is. The schools are so afraid of being sued they bend over backwards to every whim of the parents.

Little Timmy is stabbing the other kids? Better have it documented over a 18 month span with 57 different ways you politely asked him not to. Then maybe we'll consider moving him to a tougher placement.

Oh, you want to teach the Odyssey? Susie's mom thinks Zeus is actually Satan in disguise, so you have to pick something else or we'll be sued for promoting devil worship.

And then you have EdTech corps pushing snake oil so hard that admins are buying it up left and right and forcing it into the classroom against teachers' wills.

All that to say, it's a big, multifaceted problem, but the core of it isn't money. The US spends more per student than almost any country in the EU. It has some of the highest per student spending worldwide. It's not helping, and it's not because the government is interfering.