"If we fully deregulated education I bet you’d see teacher’s salaries rise."
I don't, not by a long shot.
"it’s disingenuous to suggest demand and its impact on price is “arbitrary”."
But that's not what I'm suggesting. Demand for teachers is pretty high. Pay has not risen to meet that demand, however. Demand for software engineers is also high, but only in some places has that demand correlated with a rise in salary.
It is completely arbitrary.