I am generally inclined to agree with your last point, however it is possibly to be wealthy but to have very little liquidity. It has been the case that folks in the US who are on a fixed income (e.g. Social Security or disability) end up losing their home simply because they can't pay their property taxes and eat at the same time. It's rare but it has happened and will continue to happen as long as property taxes remain the large source of revenue that they are for state and local governments.
Many jurisdictions have worked around this by allowing elderly homeowners to defer property taxes on their residence until they move/sell/die. It's a great concept, but can cause a liquidity issue should a large percentage of total property taxes be deferred for years or decades.
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.
