The belief that mining somehow "backs" or adds value to bitcoin is like a cult mentality.
It is a fact that mining somehow backs and adds value to Bitcoin. But how to explain it best? Who can help? (I am at a loss despite calling me "monetary economist" even before Bitcoin was invented

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Modern money is mostly an abstraction. It's value comes from its wide use and acceptance as value,
which is admittedly, circular logic. However, remember that the United States Dollar
was once backed by gold. Other fiat currencies are at least backed by governments.
Remove human psychology from the equation, and any semi-scarce unit could be a currency.
However, psychology cannot really be removed from the equation, since
the very concept of money is that of a medium for which to exchange values.
Proof-of-Work is psychologically satisfying because it is more "fair"
than bootstrapping a new currency out of nothing.
This has always been the case.
(I do agree with most of your comment BTW, just think you can generalize it further)