Cranking up property tax or land tax still sucks. Sure, maybe you can buy land now, but what if you want to live on it? Your house doesn't earn you income (i.e. what you build on your land is not "productive"), so you're stuck paying taxes on something that doesn't give you any fiscal value.
In practice, this doesn't help housing crises very much, but it _does_ increase wealth disparity! People who could previously afford a home now have to sell their property and either rent from somewhere, or buy a cheaper, presumably worse property.
The increased property taxes also get passed from landlord to renter, up to what the market will bear. This is also bad, because it significantly increases the cost of living.
Overall, there's no direct relationship between more expensive/less expensive housing and whether land/property is taxed. It's usually a challenge of efficient zoning etc.
Now, one alternative that I'm interested in would be an "surplus land tax", i.e., if you own a property for the purposes of living on it, there is minimal or no taxation. Then if you buy more property for some reason, the tax is significantly higher (why do you, as an individual, need more land?). This discourages people from owning a surplus of land, while (hopefully) avoiding the increase in wealth disparity. If you want land for the purpose of a business, the revenue from the business should ideally cover any applicable land taxes.