They can't be equated, for two reasons: First, "personal property" is a subset of total assets (which includes "real property"). By contrast, a wealth tax is a tax on total assets less total liabilities. By definition, they can't be the same (the property tax does not account for liabilities against that property or generally against the person who owns the property, while a wealth tax does so). Secondly, states only tax real property located in their jurisdiction, i.e. they cannot tax total wealth, which could include real property located in another state or country.

Now, you are changing your definition when you get got in a bind.

For tax purposes, my house is an asset. I depreciate it and pay
property taxes on it.

No, I didn't change any definition. You apparently don't understand the difference between a property tax and a wealth tax. You have a property tax in Switzlerand, and a wealth tax. They are not the same tax, are they? What you are describing in the USA is a property tax, not a wealth tax.

I'm trying to help you, but I promise that stops now.

Grant Thornton: "There is no wealth tax in the U.S."

They are the fifth largest accounting firm in the USA. Go argue with them.

you should be able to do without wealth tax by gifting the assets to a trust or company/offshore company and drawing down an income.

However:
You'll still have to pay any income taxes.
It might be hard to recover the assets if you ever need more than just the income (or this recovery might become a taxable event).
The US won't recognise any of this, so if they know about it, they'll tax it.

Having said all of this - this isn't advice. Go to a knowledgable tax advisor, but perhaps this will start you off with some good questions to ask.

Good luck!

Most Swiss cantons have a stiff wealth tax. Swiss residents might pay about 35% on gifts to non relatives. Swiss tax law views trust endowments as gifts.