Isn’t that sort of a circular argument? The calculations are trivial, but difficult, and only have value as proof of expended energy. That proof only has value while Btc has value, but it has no other use.

Proof of Work algorithms are not hard to calculate, it's simply designed to increase capital costs to access writing to the database (adding the next 'block' set of transactions to the blockchain).

The actual math amounts to a best effort guess in a lottery for write access to a database.

The network would function just as fast with 3-10 computers as it does with 3 billion times the amount of "computing" power.

In summary, Proof of Work is designed to waste as much energy and capital input as possible.