In economics the question "How much is something worth?" has a simple answer: what someone is willing to pay.
This answer is correct, but incomplete and overly narrow. It is applicable in many, but certainly not all, economic contexts and more generally, it's an increasingly poor measure.
Let us consider the economic question first:
Suppose I wish to sell my house - as I did recently - and I need to decide how much to sell it for, or whether to accept an offer I've received on it. For this purpose, your definition is clearly the best. I literally cannot sell my house for more than someone is willing to pay for it. The only questions are determining how much that would be (when setting a price) and whether they or someone else will give a better offer (when deciding whether to accept an offer). For this kind of simply transaction its a perfectly good measure of worth.
Consider, however, a new question: how much should I buy a house I wish to rent out for? Now, how much that house is worth is a much more complex issue. What it is worth
as an asset is more important than the transaction price. This depends not only on the cost, but on the cost of any loans, and any upkeep as well as the projected income. Still, we're sitting firmly in the realm of economics, but the simple answer "what someone is willing to pay" no longer suffices.
Move beyond these narrow questions of economic simplicity and you rapidly discover that the monetary question is inadequate. The worth of the house is much than its monetary value because it's a place to live, a place where you gather friends, have memories, form communities, shape to your tastes and so on.
The phrase "knows the cost of everything, and the value of nothing" springs to mind. Economic worth is such a narrow subset of what something is worth that is essentially useless in answering the question "How much is something worth?" in the general sense.
That this is so is effectively admitted by your quote "Economists generally assume that individuals ... are the best judges of what they want". This is known to be false. Individuals are
terrible at making decisions; people
don't make rational judgement.