Transactions cannot compose because nested transactions cannot simultaneously (1) ensure committed transactions are visible and (2) uncommitted transactions are

Transactions cannot compose because nested transactions cannot simultaneously (1) ensure committed transactions are visible and (2) uncommitted transactions are not visible. If you don't care about visibility until the end and just want nested atomicity, you can use savepoints as a kind of nested transaction, but they won't be visible to other sessions until the top level transaction is committed. CREATE INDEX CONCURRENTLY has steps where it needs to make changes visible and wait until no transactions are open from before that point, so it can't use savepoints.