Opening a bitcoin account into a banks looks similar to that opening a bank account.
Coz that is what OP asks...We are asked if we are willing to open a bitcoin account in a local bank... Most probably it is already considered a bank account..
However we consider to be our own bank, we will be controlled by some authority.
Well, that is one of the consequence that we will have to think about when we do apply for a bitcoin account in a bank, they hold your bitcoin....
For this reason there is no need for an bank to help us create accounts and help in transaction and other necessary functionalities.
Well, who knows, they might be offering something that could be very favorable to us...
Anyway, as for my opinion, I'll go for a bitcoin account in a bank, provided that it is secured and insured... Actually it is a great help to us since we will not be worrying about our bitcoin in our desktop and probably give us a good night sleep without checking if our PC for spies... Who knows, bank might offer us what they are offering to their fiat depositors...
I think one of my condition before transferring my bitcoin to theirs is they should not ask my name or any information about me aside from my signed message and theirs... No asking of where my funds came from or even asking where I am using it...