You're not wrong but this is too simplistic and avoids holding up a mirror that really ought to be held up. Zoning was the "we're gonna regulate our way into utopia" of their time. The class of useful idiots who made it happen and the class of useful idiots who will go to bat for it's continuance because they make a buck on it is far broader than that.
The benefits are huge in terms of time available and costs, and not needing childcare before or after school.
It’s hard to solve couples having two jobs in different places, but having at least one person get to work basically instantly and for zero cost is a massive boon to society.
The issue I saw is that the government department in charge of education is not the one in charge of housing and infrastructure, and there are no incentives to hire locally or make it easier to move locally. Instead you get teachers in suburb A travelling to suburb B and vice-versa, and no way that they can choose to swap roles. We lucked out.
(That doesn't mean they aren't impacted by housing scarcity in ways that disrupt the administration of school systems; they are. But the problem isn't compensation, the problem is corrupt regulation written to prop up homeowner assets.)
Changing the tax structure doesn't remove that restriction.