banks could control bitcoin in the future, they could offer security against fraud/thieves but in exchange you must deposit into their "wallet", the majority of the people in the world will follow this way, they are to lazy to secure their wallet themselves, they want everything ready to use and 100% secure
Indeed, in fact that's how banking evolved historically;
Goldsmiths had a secure vault to hold their metal, villagers would pay a small fee to the goldsmith if he kept their modest holdings in his safe.
The goldsmith would issue a certificate with fine wax seal and signiature for proof of holdings.
After a while the goldsmiths realised that the villagers never all withdrew at once, so he began to use a small amount of their gold to finance traders in the form of loans, he collected some of the traders profits as interest on the loan.
But what about the villagers now, well they were happy as long as they could collect their gold with their certificates.
Trouble only happened if all villagers tried to withdraw at once only to find the safe a little short. After a few goldsmiths got killed, the goldsmiths started to cover each others asses, if a smith from one village had a mass withdrawal then the other smiths would cover it.
Then over the years the banking industry evolved to what it is now.
There's no reason that bitcoin won't become the same.
However we can rest easy knowing that the fiat game is not possible with Bitcoin. Luckily Bitcoin can progress no futher than a fractional reserve system (like Bretton Woods).