I think it is a trust, why many coins fail? because investors none the trust and will eventually choose bitcoin. the Bank will make many rules and restrictions so that make our account be frozen.
Yes that is right if banks will start working for bitcoin then there will be the fear of freezing the accounts and if any of case occurred with any person then all the other will withdraw their money and will leave their bitcoin bank account.
But that will happen to the fiat banks as well. However, for bitcoin, people will have more freedom.