There aren't any decentralised SQL engines really. There are distributed databases that provide SQL-like abilities, like Spanner, but they're optimised for huge scale and not low trust. They're still expected to be run by a single organisation, not a p2p network of many organisations.
I am the lead engineer on Corda, which is an open source 'enterprise' (i.e. institutional/industrial) blockchain-inspired platform. But if you don't like the B word you can think of it as a decentralised database that can be queried using SQL. The intro to the technical white paper describes some of the issues with "just run a public SQL database" approach:
https://www.corda.net/content/corda-technical-whitepaper.pdf
Why not just use a shared relational database? This would certainly solve a lot of problems using only existing technology, but it would also raise more questions than answers:
• Who would run this database? Where would we find a sufficient supply of angels to own it?
• In which countries would it be hosted? What would stop that country abusing the mountain of sensitive information it would have?
• What if it were hacked?
• Can you actually scale a relational database to fit the entire financial system?
• What happens if the Financial System™ needs to go down for maintenance?
• What kind of nightmarish IT bureaucracy would guard changes to the database schemas?
• How would you manage access control?
So, it's ultimately a system that tries to address these questions and many others too. If you can solve these issues then you can suddenly actually propose an entire market putting all data into a single database engine, and at that point things can get a lot more robust and efficient. But it just wouldn't be politically possible on any sort of scale to do that with Postgres.