Think Wild Western bank robbery.
Someone hacks into their system, and drains all the coins. You're patently screwed then.
You are a fool if you choose to keep your coins in an online wallet. There is no way on earth I would do that for two reasons. Firstly, risk of hacking is very high with most exchanges and as they are unregulated and not supported by any government or institution your money is gone forever. Secondly you avoid the temptation to panic buy / sell - something too many get caught up in because of the easy access to their coins.
Coinbase isn't an exchange. I'm also hoping they would add a feature like a savings account, so there would be a waiting period for a couple days to move any of those coins.
Also, would the Winklevoss fund be insured if it opens?
The way coinbase is setup, even if someone hacked into their online server and had full access to everything, they could only access a very small number of bitcoins.
I don't think the mass of people will take the time to store their bitcoins in a paper wallet. People just won't do that.