They are not underpaid in Germany (I'd guess top 20-30% of German income) and probably other European countries.

In the US, I think it's a combination of broad-based anti-intellectualism and scorn for those who do care or service work. "Those who can't do, teach" is a phrase that's ingrained in most young people. I think many people harbor the belief that they can do teachers' jobs better, and I think the low pay seriously exacerbates this issue. When the pay is low, when schools are desperate for employees, and when you have too-stringent tenure system in place (it can be very hard to let senior public school teachers go), then you do end up with lackluster teachers. Continuing with Seattle as an example, when you have tech workers with serious academic credentials interacting with teachers who could easily make 1/10th their annual total compensation, and who may very well have far less impressive credentials, there can be an understandable sense of anger, frustration, resentfulness, etc.

I really think the solution is to pay way more. I have a math background: I did a very prestigious postdoc at one of the best applied math institutions in the world. I love teaching. If I could get paid at least $150k/year to teach high school math in the Seattle public school systems, I would jump at the opportunity. I think a lot of other people would, too. If you create the opportunity for exemplary people with superlative backgrounds to teach and to inspire young people, it will easily burnish the reputation of the schools and create a virtuous cycle enabling their improvement.

Well they have relatively low productivity and there is lot of them. Basically society can't afford to pay lot to them.