I think the myth is that just pumping more money into a broken system will fix the fact that it's vastly under achieving. The living standards of the teachers are not the issue, so much as what students come out prepared to tackle, future-wise. Of course we want teachers to love their jobs...
So you and I are in agreement that it's not really a money issue. I think lack of competition is part of the problem. The public schools feel under attack and so hunker down, trying to fight off the barbarians, whereas what they *should* be doing is fighting tooth and claw (in a metaphysical sense) to best one another, as they do in sports.
There're lots of ways to shine, to add lustre to one's reputation, if only you're allowed to step out of lockstep and develop curriculum inhouse, forming voluntary alliances with other institutions, including at the federal level.
Part of my job is to give public schools a sense that they have permission to form these alliances: go for it, teach gnu math, you'll be glad you gave it a go, and your government might actually give you a boost (maybe talk to NASA more, the NSA even?).