In no way is a property tax a tax on unrealized gains. The tax is a fee for protection of the property, end of story.
If you don't pay property tax to anyone, you must protect your own property, which is usually very inefficient.
Discussion
Insurance is a fee for direct property protection. Taxes get pooled and redistributed towards purposes that have nothing to do with your property.
It can be used to protect your property and still be a tax on unrealized gains.
Taxing unrealized gains means assessing the hypothetical sale price of some asset and demanding a payment in money as a percentage of that assessed value. This is exactly what happens with property taxes.
Property taxes are an example of a tax on unrealized gains.
Since you are paying property taxes based on assessed value not assessed value-purchase price its not really a unrealized gain tax.
Well yes, that's how property taxes are assessed, but no, it does not follow that what's being taxed is an "unrealized gain".
A "gain" is something that happens when we sell an asset for more than we bought it. If property tax were a tax on a gain, the amount we paid for the asset would have to be taken into account so as to calculate the difference between what the property is worth now and what it cost us to acquire, ie the gain. Since property tax is assessed on the total value of the property, this cannot be what's happening.
The reason people buy property is to *use* the property, unless they are speculating. So what's actually being taxed is a "realized benefit" rather than an unrealized gain.
The government or security agency says "hey, you're benefiting from that property, and we're protecting it with our guns, we therefore impose a fee that is proportional to the benefit".
I'll concede that the purchase price of your assets affects the calculation of an unrealized gain, but in my mind this makes the unrealized gain tax less intrusive than a normal property tax. It's essentially a property tax with a write-off.
At any rate, the justification of a property tax that you're using is fun philosophizing, but the revenue that property taxes generate go into the same pot as any other tax. The state isn't demarcating police or firefighting services and saying "property taxes pay for this, income tax for everything else".
You can believe in a land value tax or something as a justifiable tax, but that isn't exactly what a property tax is, since improvements you make to your property increase your tax liability. If you're justifying a property tax by pointing to government services that you consider legitimate, that's fine, but this works for any tax, so it's really a non sequitur to talk about property taxes like this.