So, I originally signed up with a local bank, which takes 2-3 days (unfortunately). This is the same model that Paypal follows.
Since there is clearly a demand for buying bitcoins _quickly_, I believe Brian is providing both a good UX for those who want to just use their account / routing numbers, while also allowing people to get bitcoins in LESS THAN 10 MINUTES (I bought 1BTC today with coinbase / wells fargo).
I should note that Mint did the same thing in order to get access to transaction history, and they had 5 million registered users as of 2011 (source: http://qr.ae/8QB9G).
If the big banks addressed the need for APIs, startups like Mint and Coinbase could do this in a more sane way, but we're talking about big banks, and in the case of Wells Fargo they actually charge users a monthly fee for using Quicken to talk to their backend.
tl;dr- Mint asked users for bank passwords and got 5 million registrations. Likewise, Coinbase is just providing a "quick" ux path for the people who want to act quickly.