Ok, but the cryptography is pointless if it's a centralized system.

How so?

Because you might as well just use an SQL database

“Proof of authority” chains are a lot more than just a database. There is still a verifiable audit trail etc.

Nothing stops you from having a verifiable audit trail in a SQL database. You could even decentralize the audit trail.

Problem with Ripple is creation of new XRPs, they had full control over that.

How do you decentralize the audit trail? Would need something like ripple

Generate a cumulative checksum of everything that happened yesterday plus the previous day's checksum, and post it in the local paper, on your website, and in all investor documentation.

Eh, last I checked the five primary validator nodes are all run by Ripple.com. Not really "POA" when there's only one authority IMO.

So, a database plus digital signatures.

so a sql database

So files with indexes... so storage devices with a file systems... so... so bits of information...

FWIW, this is how I feel about every crypto-so-called- "currency".

Don't want to get into an argument about crypto currencies, but the value proposition of BTC is different. What is not replaceable by a simple DB is it decentralization and resilience to attack, its resistance to seizure and its incorruptibility in terms of maximum supply (the digital gold / store of value narrative).

It's worth highlighting that there are distributed databases that meet all those criteria except "incorruptibility in terms of maximum supply". You're right to point out that there are a few very specific use cases that a distributed blockchain with multiple independently-owned verification nodes will satisfy and other more performant databases will not. Whether that makes them "valuable" like gold is left as an exercise for the reader.

Distributed is not the same as decentralized.

A decentralized system is a distributed system that still works _when nodes are owned by multiple different (even competing/malicious) parties_.

Exactly. In other words, a "trustless" system.

See the Byzantine Generals Problem[1].

[1] https://en.wikipedia.org/wiki/Byzantine_fault

yes, yes, I said that already: "...multiple independently-owned verification nodes..."

you hold the key to decide what to do with the funds

Which Ripple can invalidate if they control the network, which they do.