Someone went from millionaire to poor overnight when Mt. Gox failed, so it's a real concern. No one should keep their coins in any wallet except their own, and they need to make sure they have the technical understanding of how to properly manage their wallet. If your personal wallet isn't encrypted and backed up, it's not managed properly.
If you want to store coins on someone's exchange or webwallet, never store more than 25% of what you're comfortable with losing. (It turns out that "what you're comfortable with losing" is way, way more than the reality of waking up one day and realizing you've lost it all.)
This is an interesting move, but I'm worried that these new exchanges will increase the attack surface of Bitcoin's reputation. If the new ones fail, it will shake the public's confidence in Bitcoin yet again. Not that that matters, since Bitcoin seems to go along fine whether or not people are confident in it.
I don't know whether it would even be possible to insure against losing all cold storage reserves, but nobody should trust large sums to any webwallet (including Coinbase's current website, BTC-e, Bitstamp, etc) until protection against that worst-case scenario is in place.
EDIT: From the paywalled article:
The exchange could bring needed legitimacy to the currency, which isn’t backed by a central government and is traded over virtual exchanges, primarily overseas. Coinbase said it has insurance, offering traders some assurance that their money won’t disappear.
Until details about this insurance are released, do not trust large sums to Coinbase or anyone else. And unless the insurance protects against every coin disappearing tomorrow, never trust them at all. Trusting them is equivalent to gambling your savings for no benefit.