I love depositing my fiat to the banks and they are making money with it but if its bitcoin. I don't think I would avail this service but there's a possibility that it will come and they will be targeting those bitcoin investors/holders that doesn't really understand on what bitcoin is, being your own bank. They might attract those type investors by saying that their bitcoins will be safe on their hands. We know on how the banks are doing well in making money.
I too love depositing my hard cash in bank and enjoy the interest over it but if bitcoin deposits starts I dont think I will be excited enough to invest my bitcoins in it knowing that the banks method will be very new and vulnerable to multiple threats rather if needed to invest I would love to turn my bitcoins into fiat and then invest them in bank and feel the relief that my money is safe and increasing there. But maybe in future if the bitcoin depositing feature comes and seems promising to me I might try it too.