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Literally everything good that humans have produced are proof of work. Proof of stake is the rent seeking that comes afterwards.

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I have no notion of what metaphor you are referring to. In real life, POW is a waste of electricity that produces nothing external to proving that CPU cycles were wasted, with an ever-increasing difficulty in the case of Bitcoin (getting worse with time, on purpose)

Not a metaphor. The general theory of relativity is proof of work, so is a bridge. Being too big to fail is an example of proof of stake in a system and how it can be gamed.

> an ever-increasing difficulty in the case of Bitcoin (getting worse with time, on purpose)

This is not how Bitcoin's difficulty adjustment works. It increases/decreases with the value of the block reward. This is proportional to the value of bitcoin, transaction fees paid, and decreasing new bitcoin issuance. Bitcoin users pay miners for their PoW because they find the value of using such a system to be worth the cost.

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