Not everything follows the rules of capitalism, especially when public school teachers are paid by the government. There are giant teacher shortages across many locales in the US, so according to you we should see skyrocketing teacher pay, but that hasn't happened (pay has gone up in some locales but nowhere near the amount needed to fix teacher shortages).
The government doesn't have traditional shareholders like a corporation. Obviously they have their citizens as shareholders of a sort, but at the moment it feels like the loudest groups are prioritizing budget over outcomes.
Not everything follows the rules of capitalism, especially when public school teachers are paid by the government. There are giant teacher shortages across many locales in the US, so according to you we should see skyrocketing teacher pay, but that hasn't happened (pay has gone up in some locales but nowhere near the amount needed to fix teacher shortages).