The beauty of bitcoin is that we do not rely on banks to lose our money. We are our own banks. Would you really trust banks with your bitcoin all be it the same can be said for fiat.
Correct! That's exactly the point of using Bitcoin in the first place. There's no need to trust Banks because you're your own Bank when you make use of Bitcoin. Allowing Banks to take control of your Bitcoin may not be the most ideal solution, since you're adding a middleman or a custodian to manage your funds (whereas Bitcoin was designed to counteract against this).
Whenever Banks decide to offer Bitcoin for deposits or not, we're yet to see since there are many Banks which see the original cryptocurrency as a threat. In addition, Bitcoin is volatile and super risky for Banks to adopt it as a serious investment. The probability of a Bank offering Bitcoin for deposits becomes lower each day, because of Bitcoin's unstable price and unregulated environment.
Therefore, Banks would look for other cryptocurrencies which are stable in value such as Tether or even bitUSD, but not Bitcoin or other cryptocurrencies where their values are driven by speculation.
