Your analysis encapsulates the intricate dance between a player's cost and their attributes. Indeed, the value of a player is a composite of various factors, including their proven skill set and the reluctance of their former team to let them go. This valuation dance extends beyond the field, weaving in aspects like health and age. A player's durability and youth contribute to the allure, prompting teams to invest more with an eye on potential long-term contributions. The interplay of these elements, encompassing skill, demand, and physical condition, creates a complex tapestry that defines the price tag during transfer negotiations. It's a fascinating dynamic in the ever-evolving world of football transfers.
Teams that buy a player are actually the ones deciding the value of a player. A player who is not sold, has absolutely no set fixed value, you can consider a number fair to you, but it will never be true. The moment a team buys a player, they are showing what their value is, by paying that much.
So, when Bayern paid 100+ million for Kane for example, they basically said Kane worths that much to them, they are willing to pay it because they think he worths it, that's what decided his value. You could say he worths less, but Bayern disagreed and what a team spent on a player decides the value far greater than what some other person thinks that player worth. What I think his worth is has nothing to do with reality, only Bayern and their money can decide his worth.
That's correct for the most part, but I am sure that during negotiations these clubs are aware of the offers that a player has from somewhere else. In essence, yes if a club pays X millions for a player, then that player is worth X millions. But Bayern knew that Kane is worth that much because there were other clubs involved that also tried to convince him with a high salary and to convince Tottenham with a similar transfer fee. Most of the time the public market values are quite accurate although there is no doubt that some players are overpaid both in salary and the transfer fee. There are a few examples that still make me shake my head. One of those examples is Dembele who was bought by Barcelona from Dortmund.