ECB isn't even a miner. The Euro is more like a token that the underlying company keeps on making more of. With the simple difference that their value always stays at 1 Euro. So inflation is at play with the Euro. Blockchain would likely be a good way to battle inflation while it is being traded against fiat currencies in order to obtain utility. If we were to have a fully integrated blockchain world I would imagine that there would still be some inflation but a lot less than now.