Most countries dont have such high property taxes that the USA does. In London I paid $2500 a year in council tax and thought that was a lot of money, even though that was about 0.25%. Meanwhile NYC suburbs I'm now paying that every two months.
My aunt and uncle used to live in Bronxville, a suburb of NYC (it's part of Eastchester, which is in turn part of Westchester... NY municipal areas are confusing). They moved out in 2003, in large part because they were paying $25k/year in property taxes and they were both retired empty-nesters.
When they told this to me and my mom, we both thought it was insane. I was born in Texas, and my mom has lived in Texas since 1979. I'm not a homeowner myself (I rent a townhouse), but my mom is, and her property taxes in Dallas are around the same as what you paid in London.
This is one of the reasons I intend to stay in Texas for the rest of my life. Northern coastal cities are just completely insane in terms of expenses. New York is a wonderful place to visit, but I'd never live there.
It makes no sense to live there when you have no school age children since you can move a few blocks away in one of the surrounding towns and still have the quality of life.
Where I live, you have to be 65+ and own 60+% equity in the home. The problem is that some old rich people are moving in, paying cash for property, and then deferring. They aren't exactly the intended beneficiaries of the scheme.
If you want to tax idle wealthy people, it's simple: tax their investments. This means a stock transaction tax, since so much wealth is tied up in stocks. You can also tax additional real estate properties (i.e. no property tax for a primary residence, but tax vacation homes, rental houses, etc.).