Everything is possible, and I believe a time will come when the bank will be the biggest and safest exchange because Bitcoin is still growing. We can see how many countries are accepting Bitcoin and also developing a Bitcoin reserve.
If the governments are now friendly with Bitcoin, then it is possible that one day the bank will have something to do with Bitcoin, and it will be a great advantage to the bank because the bank will be more reliable than online exchanges. There won't be cases of theft and scams like what is found on online exchanges. I'm very sure that in a short time, we can have this.
Even if this happens in the future, I don't trust the banks, they don't believe in decentralization so I don't buy this idea, government apparatus can never be the safest exchanges, satoshi has a reason for making Bitcoin decentralized, the government and there institutions can never be trusted, even though we see it as a welcome development that many nation now have interest in developing a Bitcoin reserve, I think things should be as it is, as a matter of fact it seems we are even overthinking, till when they accept what made them look worthless then I can further discuss about this.
Sometimes am even skeptical if the government of most countries are actually embracing Bitcoin or there's another agenda underneath, EL Salvador came out very open to do the needful, I think others are still playing politics for now until we see them do the needful,