This is basically what the banks, and companies like PayPal, are starting to do right now.

They are starting to offer their clients the ability to exchange their fiat for Bitcoin, held in their own system.

They're promising ease of use, but the problem is that you cannot withdraw those bitcoins into your own wallet.

In that way, banks are trying to keep relevant, because in reality you don't need the banks to hold your own bitcoin, you can just keep it in your own wallet.

Bitcoin doesn't need banks, banks need Bitcoin to keep themselves relevant.