We could pay teachers even half of the median salary for HN users, and then see if outcomes improve?
Nope, it's been tried before and it had 0 affect on student outcomes. I'm not saying that teachers don't "deserve" more, but it is not going to help students one bit.
And when the outcomes don't improve because money isn't magical, we could double the salaries again! And again!
Seriously, how do you think that will work? Are you suggesting that the teachers could improve outcomes now, but are holding out as some sort of negotiation leverage? Or that there's some secret corps of millions of super-teachers who could educate the nation's children, but who would rather be network technicians and underwater welders because they need that half-median software income?