Yes but it is worse than that. The fact that they are paid by the government the incentives are for them to push for more and more money instead of what the rest of the world works under... market demand from customers.

Because of this their influence affects all politicians not just democrats. A republican, even one that is aligned with libertarian ideals will get roasted if they even hint at something negative for this block. They will get buried. And because the public has been brainwashed into thinking the problem with education is we aren't spending enough money it works. So they impact every politician. Even your favorite "conservative".

The incentive structure is the core issue not politics. The only solution I have heard that would work is that anyone that gets paid with tax dollars doesn't get a vote. Or at least their vote is less significant from those that do not get "public" money.

That will never happen.