I think, if the bank accepts us to send a bitcoin then this is pretty good, everyone has no worries about securing the key to keep the bitcoin current. This bank will take care of us. But for the bank to keep the bitcoin is high security and it is hoped that blockchain will solve the problem. But I do not like it much, I still want to keep the bitcoin myself and send fiat to the bank, they can still make a profit from this.
The main thing is that investors want to put bitcoin to the bank does not. That's the important thing.

Everything is possible, but this will take many years, because we see bitcoins for 10 years already, but there are no relations with banks at this time, it is only to hope that the governments of all countries will legalize the cryptocurrency and then the banks will start cooperating.

Look we all know that bitcoin is a decentralised crypto currency and there is no such authentic regulating body over the bitcoin and this lacks the control over all the bitcoin activities and thus leading to increasing illegal use of bitcoin like selling drugs, explosives and money laundering and many more and therefore the current emphasis is in how the entire world accepts bitcoin and the countries who are in against of bitcoin should legalised it in their nation, acceptance of bank is secondary.

According to my point of view banks will never offer bitcoin deposit because bitcoin decentralized in nature. And one thing more Banks find crypto as a major competitor. Let us suppose if banks start depositing and how banks earn income because banks earn income from interest paid by loan holders.

I think this will come. It might not come now, but in the future it will. Bitcoin has a part of the lives of many people.Indeed, bitcoin is different from fiat money, hence, it needs other mechanisms.

For now this is not going to happen as the two seems to be in opposition but I strongly believe a time will come where there will be an integration and banks will begin to offer bitcoin deposits.

I do believe that in the future banks will offer this kind of thing.
They will be accepting cryptocurrency deposits.
.
But as a holder i dont think it will be beneficial for us to rely on banks for the safekeeping of our cryptocurrency assets.
First of all we will be doing against the aim of crypto which is to create a decentralized form of currency.
And by giving banks the ability to do this then its as if we are just getting back to what has happened with our fiat.

According to a report issued by the Financial Time https://www.ft.com/content/ca0b3892-a201-11e7-9e4f-7f5e6a7c98a2
A few major Japanese banks are already started working to create their own cryptocurrency called J-Coin. Mizuho Financial Group and Japan Post Bank are getting support from the Japanese central bank and financial regulators to launch their project. There is always a possibility to banks offer bitcoin and cryptocurrency deposits.

I think we will see this in 2019. When banks realize that people are ready to climb into loans to get bitcoin. They will offer such services. Even if people will go into the negative, if the price is inflated taking into account %

Precisely because Bitcoin is too risky for banks, banks will not perform other operations with Bitcoin or other decentralized crypto currency, except for providing services for their exchange into ordinary currency. Bitcoin has too much volatility for banks to accept deposits, or give out a loan in the crypto currency. For banks such a high risk is not appropriate. They have so many different schemes of doing business without such a risk.