That rule about paying the full amount on year one is... odd.
[1]https://www.boe.ca.gov/proptaxes/homeowners_exemption.htm
This is generally solved by limitations on bankruptcy that prohibit you from being kicked out of your sole home due to debts, tax or otherwise, except if that house was bought on a mortgage.
However, there are certain advantages to taxing specifically wealth (as opposed to income or consumption), and a huge proportion of wealth is in real estate, for very many (I'd say most, but I don't have the exact stats) people the majority of their wealth is real estate, and it does make sense for people owning a much more expensive property to pay more taxes.
And of course if you sell the property, no matter what there should be taxed earnings.
For limitation rules, I think they a part of the problem.
If you for whatever reason are on a financial decline, property tax adds to the kick in the face until you reach the very bottom.
Then if you manage to begin crawl back out of the abyss, that boot will start planting itself repeatedly your face again, stopping you on your way back to normal.
....So, y'know, not helpful for 99% of all homes in America.
For example, if you want police, fire department, schools, sewage and water supply, etc., it makes sense to tie that taxation to your house directly since those are features and benefits of where you choose to live.
What's happening in Texas with valuations seems absolutely mind-bogglingly stupid though. When you have neighbors with identical lots and similar single family homes valued 200k+ difference in property valuation, there's a problem.
True, but that should be addressed with income tax, so that situations like losing a job for some time (not that impossible these days) doesn't force someone to sell the house.
In my country the main home is exempt, but from the 2nd one on there's a property tax on which I fully agree. I would go even further and tax more the 2nd+ houses that aren't offered for rent, so that there is enough offer that the demand doesn't drive prices up also for houses for sale.
That may be a local phenomenon having no equivalent in the US, but I observed the tendency to keep a lot of houses empty and unused, some well connected construction entepreneurs build entire condos then keep them empty for years after they're completed. My only possible explanation is that they're keeping the offer low in order to keep the demand high, therefore driving or keeping the prices up. Well thought taxes should address this problem without hitting the poor, but some of those people are so well connected with politicians that this is not going to happen anytime soon.
Property taxes may work fine for the FAANG-employed high income citizen, but it is a way worse deal for medium/low income as well as retirees.
If you own more than one apartment/house and don't use or rent out the other.
Second, companies owning apartments/houses.
Ah and third, property with foreign owners (not immigrants ofc but owners living abroad buying up property in the US).
I'm not trying to come off as a communist or something, I just believe giving the widest opportunity for people to have their own home. So even if you are broke as a rat, you still have a place to stay safe.