It would be nice if I could buy cryptocurrency with my account funds, and for it to be protected/insured while it was in the bank's wallet. The ability to transfer in and out, etc. The ability to make debits against a cryptocurrency balance, etc.
I use robinhood at the moment. If robinhood was able to act more like a bank, and supported transferring cryptocurrency in and out, then it would basically be what I was looking for.
In the past I've just used coinbase/poloniex, and I just transfer to my wallets. I currently use bitcoin to buy domains on namecheap, and I use purse.io to buy stuff from amazon - but I can see myself using it for a lot more in the future.
There may not be a lot of demand for it, but like I said, if local banks started offering these services it would get my attention.