What criteria are used to value collectibles?

Let's say you've saved a rare banknote, coin, or other collectible.
After some time, you decide to sell this collectible.
You go to a dealer and ask him to appraise "your treasure."
What will he tell you?
I'll tell you right away: he'll value it far below its market value.
Wherever you bring your item, these organizations operate on the principles of pawnshops. We'll give you something, and be grateful that we condescended to give you something.
For some reason, these people believe that if you come to them, you're in need of money and will give them your item for free.
Who could agree with such an "appraisal"? Only someone who didn't collect it, didn't keep it, and who stole it! In a Soviet fairy tale film, "An Old, Old Tale..." (a version of Andersen's "The Tinderbox"), a soldier is on trial.
The king addresses him: "Our kingdom is small, so I hold several positions! As 'prosecutor,' I convict you! As 'defense attorney,' I find no mitigating circumstances! As 'judge,' I sentence you to death!"
The soldier asked the king: "Perhaps you also act as executioner?"
The king replied: "No! Someone else 'works' as our executioner, and you'll meet him soon!"
Why did I give this example?
It's bad when one organization acts as both appraiser and buyer!
You might say that you can take your item to a company that exclusively appraises collectibles!
That's right! But to do this, you'll have to pay that organization! The fee could exceed the value of your item! Let's assume your item was fairly appraised. But that doesn't guarantee it will sell for that price!
But sometimes things are overvalued, when items are unreasonably considered expensive when they really aren't!
All sorts of junk sells for outrageous prices at auctions.
A banana bound with tape sold for $6,000,000.
A sheet of paper with a printed tin can sold for $1,000,000.
An empty painting frame sold for $77,000,000.
Russian oligarch Mr. Alikhperov bought a "Konstantinovsky Ruble" at a Western auction for $2,100,000. He paid the equivalent of 40 kilograms of gold for 20 grams of silver! According to the catalog, this coin's value is 10 times less!
Therefore, it's impossible to talk about a fair appraisal with such approaches! There should be uniform appraisal criteria! This discredits the valuation of collectibles!
One dealer told me that everything is determined by a person's desire and ability to possess these items!
Rare coins and banknotes are valuable only to the collector; they have no value for anyone else.
I believe everything is determined by a person's desire and ability.
But there are things that everyone considers trash! Why are they valued so highly?
This discredits collecting!
Look at which paintings are worth the most? They're not Rembrandts!
My opinion is that if you've saved something and other people haven't, then you already own a small treasure!
The value of objects should be determined by mathematical probability!
The lower the mathematical probability of collecting and preserving something, the higher the value of the collectible!
But, of course, everything is determined by a person's concept of harmony, desire, and financial ability!
Another problem is how can people directly exchange and offer their collectibles to others without intermediaries?
Why does everyone buy at auctions and in stores? They don't guarantee anything!
Are there people who are actually interested in anything, or is it all just an illusion?
Why is all this necessary?