If anything, it's almost obvious that almost all American public schools are, in general, "underfunded".
Part of having a free market in labor (such as we have) means that, if you're trying to attract people to take on a particular position, you need to offer enough to lure them away from their other options.
Public school teachers have good job security and benefits (after awhile), but the starting salary is usually very uncompetitive with most skilled private sector work and it takes a long time to obtain enough seniority to catch up.
For a lot of folks who might make good teachers, switching to teaching in public school is asking them to take a paycut in the 50-100k+ range.
If you don't have starting salaries for teachers in the 60-90k range you lose a lot of people to law school, medicine, technical fields, grad school, finance, and even other public sector work like police and fire and so on.
So rather than asking "is school underfunded or overfunded?", a better starting point is:
(A) what would it cost to get the people we'd want to be teachers doing the job at a level we'd be happy with? We don't have to resort to guesswork and rhetoric here: think of people you know, and figure out what the pay would have to be to get them to take up teaching instead. That's your answer.
(B) Once you've figured out what it'd cost, then you can start figuring out "is it worth it?" Most people jump in with a particular agenda to push and never do the gut check "would anyone I know who's capable of being a good teacher work for 45k starting?".
There's certainly a lot of bureaucratic overhead that could be reduced, if the political-economic cost of reducing it was outweighed by the benefits of doing so; that's another fact-based question you could derive answers to with some real legwork.
If anything, though, the above highlights one of the less-discussed issues with "rising income inequality": as the best "attainable" private sector outcomes become increasingly more attractive than the best public sector outcomes, you either have to spend a ton of money to get anyone to take a public sector job or you have to settle for only incompetents and failures going for public sector work; witness also, eg, the SEC or FDA.