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But that is the conundrum. If the "work" is not really worth anything to other people, then the work isn't useful. If it is useful, it makes attacking the blockchain free. The security is because the work can't be used for anything except securing the network.

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As long as the work is as useful to everyone equally (regardless of who mines), then it still works.

For example, if it were solving an incredibly complex mathematical or scientific problem that benefits all of mankind - then the incentive is equal for everyone.

which is the premise of Primecoin, IIRC.

It looks good on paper but doesn't work in reality, bitcoin just works..

Are you claiming that anything useful that requires thermodynamic work can be monetized? You may be right but that isn't obvious.

It's a simpler claim than that. The claim is that anything useful can be monetised.

If you come up with something useful, but noone is willing to buy it at any price, what's your basis for claiming that it's useful?

If the useful product is intellectual, and proving work involves publishing the product freely, how do you monetize it? Selling support contracts a la FLOSS?

It also happens that both these conditions (intellectual product + must be published freely) are the typical approach of PoW blockchains.

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