Exactly. Surely the finance industry can come up with a product that automates this so you automatically sell them a tiny slice of your home to make up the property taxes without it affecting your cash flows.

The private finance industry need not be involved.

Just have government allow taxes to be deferred until time of sale with interest pinned to the cost of borrowing for government. That already exists where I live for people over the age of 65. The government can still get the revenue for free via borrowing and the payback is more or less guaranteed.