Of course you do. You don't get a bill that says, "you made $100k and here's your tax bill for that," but you do get a bill that says "your property is now worth $200k and here's your new tax bill for that increased valuation."

You're paying a higher tax because you possess an asset whose value increased, even though you've realized none of the gain.

That's pretty obviously the point being made here.

No. Look, if OP wants to suggest a wealth tax, I think that's a concept that can usefully be debated. They're not without precedent; France has had one, off and on, for many years, and sure, property taxes are closely equivalent.

If OP wants to suggest a tax on (realised) income, then, well, we already have that. There's not a lot to debate here.

If OP wants to suggest a tax on unrealised income, that's a pretty silly idea with enormous practical obstacles. Also, it is fundamentally not a wealth tax. It is different in every particular; one is a tax on a stock, and the other is a tax on a flow; they are charged at different times, on different things; if an asset declines in price, the wealth tax levy declines, whereas an unrealised gains tax would...what, have to issue tax credits to be carried forward? The whole thing is unworkable.

(And even if it was workable, it would be in principle and in effect, vastly different than a wealth tax.)

I understood him to mean that your annual property tax bill is usually a proportion of the property value, and increases with the property's value, and that's a precedent for doing something similar to other property like stocks.

Why is it an inappropriate analogy?