Mint asked for bank passwords, and had 5m registered users as of 2011. They sold for $170 million. I believe Coinbase is copying common UX patterns which have been proven to be palatable with users.
Coinbase is neither Mint nor Paypal. We have no idea if they will survive 6 months, and we can't trust they don't store credentials on their servers, even though they say they do. Have they been security audited? Or do we just take a one-line comment on Hacker News as the truth?
If they reach a level of legitimacy, then maybe it might fly with some users. But I personally think it's way too premature to ask for usernames and passwords for banks, especially given how much fraud, hacking, security problems, and monetary loss associated with Bitcoin companies.
