[charadeyouare]

Bitcoins can't be printed out of thin air. People can't own billions of them. Yes, you're missing something.

New bitcoins are generated at a fixed, hardcoded rate. First off, the software can't be changed to emit Bitcoins at a different rate just because banks might want to.

And if the software is changed to emit Bitcoins at a different rate, Bitcoin owners will say "Hey, this changes the rules, it's not fair, I'm leaving." They'll sell their Bitcoins and buy some other cryptocurrency that didn't change the rules.

With banks you can't say "this isn't fair, I'm leaving." With cryptocurrency you can.

[ephbit]

Your're missing the point.

OP writes about banks handing out Bitcoins that don't exist on the blockchain but only in the banks' databases. So the subject of mining is mostly irrelevant here.

As long as people trust them, banks can very well inflate Bitcoin.