We enact zoning laws with consideration to what we're being taxed to live and work in a high-demand, low-density environment.

If a tax on holding onto unimproved land is nearly zero, we're very likely to implement zoning laws banning development, because citizens have little reason to change things. But if the holding cost increases, (say with a significant Land Value Tax) folks now have a reason to legalize development.

...Californians should consider the role of Prop 13 in its current housing crisis.

They do, but detractors of Prop 13 also need to remember why it was enacted. Property taxes were skyrocketing, and causing people to lose their homes. Homes they had lived in for most of their lives. These people had done absolutely nothing wrong, except choose to buy a house in a place that later became very desirable. Any solution that does come up should not cause people to be forced from their homes because they became too expensive, or because other people with more money want it.

From my perspective, if new tenants are willing to contribute more to society to live somewhere, that should trump who was on the land first. When they sell, the original owners are well compensated by appreciation in property value.

Artificially suppressing property taxes to protect entrenched owners is a lot like taxing the internet to support newspapers and record stores.

So to you, money trumps all? What if those with more money simply wish to buy the house as an investment, so the people who live there not only get chased out, but the house sits idle?

Implementing a tax on the land would remove the tendency to speculate upon it.

Currently, why do people buy real estate as an investment? It's not because they believe the actual building materials will become more valuable, but rather that the land will. We see far more of "land banking" than speculation in commodities, insofar as commodities tend towards marginal cost.

Anyway, if a land value tax is in place, the land value increase won't be captured as profit, and thus all locations will only be used by people who mean to use them.

There is no reason to believe that middle class residents will be "chased out." However, we would see market incentives that would lead to gradual densification in residential areas that are encountering rising demand.

Then clearly the property taxes aren't high enough.

There's a fairly good solution. Start charging everyone the same tax, but the amount they pay will follow the old prop 13 rules. The rest will be a special lein against the property. You may optionally pay down the lein, or simply wait until the property is sold, when the lein is settled from the profits. Then add in some exceptions for the value going down, and maybe a reduction if the extra is paid early.

Then you won't have people hold on to inventory just for the taxes, and eventually things will even out as people sell each year.

Plus local governments would be able to borrow using the value of those liens as collateral to fund current operations.

Yes! Excellent point that I hadn't even considered.

The plight of a person in such a situation should never be discounted, but it's simply not a viable option to guarantee any land holding to be held in perpetuity regardless of ability to pay for its rent. If you ration off land this way (quite inefficiently, that is), you cease to have enough land for everyone else. Which causes a class of suffering far greater than granny deciding to sell out, and move to a condo.