If Coinbase (already holding peoples coins) is one of the reasons because people like other people to hold their money, then why do you think we need another bank?
We need another bank to compete with Coinbase, of course.
We have circle and we have many exchanges that work in very similar ways that coinbase works.
While I personally think that if you want to allow a third party to control the private keys that hold your bitcoin, that coinbase is likely the safest service to use, this is generally a very bad idea, especially for larger amounts