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What problem does that solve? Fiat money is clearly better than Bitcoin, easier to spend and use.

Yup. The only fields where Bitcoin et al have an obvious advantages is scams, fraud, speculation, money laundering, and a little light drug crime and extortion. Bitcoin has many theoretical use cases, but possibly none that are legitimate, socially useful, and in practice better than alternatives. And we've had nearly 10 years for those uses to appear.

Also: it isn't particularly efficient at these tasks. Proof of work mining has been discovered to have a major flaw AND it doesn't scale well.

I'm sorry, I don't know of one. But that doesn't mean PoW blockchains are actually reliably doing this either.

Any database that only allows appending, and is public readable?

Digital signatures have been a thing for ages.