I'll give you housing though. One of the reasons housing is expensive, though, is because it is closely tied to job opportunities.
Public spending on infrastructure and services raises land values, as parks, police, and fire departments make locations more attractive to live in. This subsidizes landholders and allows them to charge higher rent whenever these services are paid for by a tax on labor rather than a tax on land.
With a land value tax, landholders have to privately invest in improving the private property on their land, such as expanding the supply of housing units, in order to increase their profits. Without a land value tax, landholders can earn greater rent and profit without actually privately investing in improving their property. They simply have to lobby for higher public spending paid for via taxes on income or consumption and then they can raise rents without competing to improve their supply.
This sounds like how the property tax works today.
At municipal level, where a property tax bill is comprised of (a) land value, (b) improvements and (c) special assessments, which are voter-approved voluntary taxes to pay for things such as new tram line or a pump for the water district.
The land value periodically gets reassessed to account for improvements, public services, and general real estate prices in the area.
How does your system differ from the property tax status quo?
There would be no sales, earnings, payroll, income, excise, personal property, tariffs,state, or federal taxes for residents. Residents in land tax counties would only pay the single land value tax to the county assessor. The county would then pay negotatiated state taxes on behalf of its residents, and ideally the state would also pay negotiated federal taxes on behalf of its counties.
There isn't some sinister cabal of teachers, that restricts supply, for the purposes of keeping their wages high. There isn't a grotesque system of receipts payable, and the user not paying the real price of service, and hidden, unitemizable fees at my local high school (Two of those do, however, start appearing when you go to university.)
There is more then enough education to go around. The problem is that it's not evenly distributed. I'm not talking about sending every kid to Harvard, here.
Healthcare certainly has people restricting its supply, but also has the exact same problem. We have the budgets for it, we have the doctors, and nurses to provide it - but we don't provide it very evenly.