Homeowners carry most (unless the mortgage fails) of the risk around housing prices. If a town goes to crap and a $500K house drops to $250K, will society then help cover that loss?
In 2008, the banking system imploded. Owing to a number of things, but primarily securitized lending leading to too many bad loans, losses in the banking system exceeded the amount that could be absorbed from loss provisions and profits. (Which as point of reference, isn't that high to begin with, it's no more than about ~0.75% of total loan capital/year).
The US (and other countries) did two things - they bailed out the banking system's asset losses, and they lowered interest rates.
Had no intervention at all occurred, there would have been a great depression style crash. That would have led to substantially lower house prices (due to the destruction of money/credit) - but it would also have destroyed anything else in the economy that depends on credit.
Had just the asset side bailout occurred (this is essentially Quantitative Easing), and interest rates been held high - housing prices would still have dropped. Lower interest rates translate directly to being able to afford larger loans, larger loans mean non-linear (leveraged) higher house prices in any market where housing is in any kind of scarcity/high demand.
Now it could be argued that it was necessary to do both to stop the banking system failure from destroying the economy - but in that case, and with house owners clearly benefiting preferentially, why wasn't some form of compensation advocated for all the non-house owners in the economy?
But the 64% who benefited is a whole lot more.
Apropos not a lot - this is also the reason why real estate in places like London, SF, Vancouver, has become the 'store your wealth' option for the very rich.
If land tax were, say, 10% of land value, then buying a house would be at least an order of magnitude less capital intensive, and the homeowners capital risk would therefore be much less significant.
You're questioning whether we should have property taxes at all. As long as we do, the principle that property owners share their gains with society is established. And certainly, if property values fall, taxes should (and I believe generally do) as well. So to that extent, it already happens.
Governments need a certain amount of money to function. The question is, what is the best structure for the taxation system. Should we tax property? Income? Consumption?
There seems to be general agreement among economists that a land value tax is the least inefficient form of tax. Read Henry George if you want to know why.
Hell, a flat wealth tax proposal might even get the support of economists.