Even places (like California) that do not assess tax based on value still have massive fleets of property value assessors that are used during the course of normal market transactions, since those who lend mortgages use them to prevent fraud.
A 50 year old building, with old systems, may be fully depreciated, but if one had to rebuild, one would need far more than the current building is worth.
When one buys a home with a mortgage, the bank requires an appraisal. In some places, the forms don't even break out land value from building value, or they do it badly. An appraisal merely compares the subject house with others that have sold recently in the same area. Better location? $15,000 more (or, in California, $100,000 more) Inferior location? subtract $15k or $100k. 1 more bathroom? Add $5,000 (CA: might be $5k or $50k) new kitchen vs 20 y/o kitchen? Add $10k, $50k or $100k, or more, depending on what is typically spent in that neighborhood. For each "comparable" add up all the pluses and minuses, and add that to the transaction price for that property. Average those, and the subject house value is estimated. Land value is in there, but not explicit.
California has assessors, too, who, after a property has sold, update the assessment on it to equal the transaction price. Some goes to land, some to the building. (check out listings at realtor.com, and fully expand the property history info. Notice when the previous transaction was, and look at the increases. They are in reality mostly land value. Buildings don't appreciate. Land rises and falls in value --- mostly rises.)
But appraisers and assessors are very different.
Valuations in currency are an abstraction for how we deal with this really tricky and intractable problem. But like all abstractions, it's leaky. A $100 bill has no "inherent" value yet it's value is very precisely known.
So you see, there is no inherent value or price to oranges or water or land, or anything. This is a fundamental misunderstanding that Georgists have about the nature of prices and the world.
The fact that someone can be appointed to declare an imagined inherent price to water or land or whatever doesn’t change it. Yes, the government does appoint people to do this and it is ridiculous. My house isn’t worth what the government says it is, it’s worth what I’m willing to trade for it.
What you are arguing against, the idea of taxing something based on its "value" where everybody already values things differently, this is not a new thing. It's not hard to implement. We already do it. It's here in the real world. We have property taxes. Each property is unique, non-fungible, everybody has different valuations for every property, and yet somehow we still work out a "market" value.
Establishing land values is only a slight modification of establishing property values. It's easily solvable, and the places that have implemented it have not had difficulty establishing the valuations for tax purposes, by basing these valuations off of market transactions.
But, you might argue, what if your personal valuations are different than what the "market" values them at? Well good for you, because then you are likely able to find a great deal more value out of a property than what the market values something at.
And maybe if the market values something far less than what you value something, then you can hold on to it for cheap! And if the market values something far more than you value something, you can avoid the expense of buying it, or if you have it, you can profit from selling it.
If markets are useful for something, it's finding out what a population thinks something is worth. When it comes to land, and who is excluded from using this precious and finite resource, and who is allowed to use it, market valuations are extremely useful. We can watch transactions to figure out who is using up the most of what other people want (i.e. holding land with high market value). If somebody is hoarding a precious resource, but unwilling to pay the taxes to hold onto it, perhaps they don't actually value that resource so much after all.