Earlier quoted context omitted.
I'm not sure what you mean by "recreating the frontier?" Are you talking about cities, suburbs, or rural areas? Changing property tax rates doesn't change cities or suburbs into something else, at least not at first. All the property is still owned by the same people. People still live in the same houses.
Perhaps I'm explaining it poorly, that's entirely possible. The frontier is where land value is zero, at the margin of production. It is possible to get value out of the land, but only with hard work. Currently this land may be held without using it for production, but it largely doesn't exist. This is because the lack of a land value tax incentivizes landholders to own all land for the purpose of speculation rather…
A Manhattan where the property owners pay huge taxes to the government (because that's what it would take the drive the land value to zero) would still be an extremely expensive place to own property. This might be a good way for the government to raise revenue, but it's not really a "cheap land" situation. It's one where the government is effectively the landlord and everyone pays high "rents" to the government.
It's plausible that such a scheme would lower the cost of living in some places when it's due to speculation, by popping the bubble. But it doesn't lower the cost of living when it's due to the fundamental value of owning property there.