1) Accountability - I believe users should know when I mint coins. They should also be able to verify that no double spend is possible
2) Extensibility - By having all transactions public, it's much easier to build integrations on top of CC
Your structure isn't a blockchain though. Transaction 0 does not indicate where the original coin value came from (there was no "minting" transaction).
So users can't actually verify double spends.
Then you can verify double spends
If you know that, and your users know that, why not just keep transactions private like PayPal.
It's no different than when the NYT changes their article. People have screenshots and can show the discrepancies.