you are exactly right, but everyone will be using it, as all fiat will go across this blockchain
I doubt it.
If you operate a backed currency you're far more efficient using a secure SQL server as the banks will soon find out to their cost once the "we're blockchain friendly" bandwagon gimmickery has worn off.
The whole point of a blockchain is that it's designed to support peer-to-peer, unbacked tokens. Ergo, it's not much use for transporting non peer-to-peer, backed ones. Even if it does shave something off their clearing expenses it isn't going to change the nature of their money which will still require willing debtors to queue up and underwrite it with their future labour. (And those are in increasingly short supply).
You would be surprised by how many different attempts are in the making in "the blockchain world". These people are trying to use a blockchain nearly everywhere and for anything.
I mean I agree with you when you say that the whole point of a blockchain is that it's designed to support peer-to-peer, unbacked tokens but this does not prevent them to find other possible use cases.