Would it be a crazy idea to have central banks set the rate of a land value tax to target stable nominal land prices?

Economists broadly support lvt as an efficient tax, and at least 5 Nobel Laureates have advocated using it to socialise all land rents. However, one of the biggest issues with implementing lvt in a serious way is the fact that it lowers land prices. In isolation this may be a good thing, but given how many people have mortgages, and how highly leveraged banks are with regard to land prices, implementing a large lvt overnight could trigger a financial crisis.

Instead, what if the central bank is given the power to set the rate of lvt in order to keep nominal land prices stable. This would allow the tax rate to increase slowly over time without putting people underwater on their mortgages. As a result of inflation, land prices would steadily decrease over time in real terms, slowly unwinding the financial system's dependence on land prices without causing a sudden shock.

I've given this approximately five minutes thought and I'm not an expert in banking, finance, or economics, so I'm sure this idea is riddled with holes. What are the flaws in this idea, can they be fixed?