Further, Coinbase does give users access to their private keys with the multisig vault, so one of your two criteria has already been met.
Since Coinbase has a large cold storage reserve, and since multisig-protected coins can't be put into cold storage, the answer is pretty clear: Coinbase protects few people.
It's a false dichotomy that coins must be stored in a personal wallet that users mess up, or a webwallet that exchanges mess up. There's a third option: Convert those coins back into USD and stick it in a bank. As long as you're storing less than $500,000, you're guaranteed to have it.
Anything else is pure greed. As someone who has been burned by greed, my misfortune stands as a warning to others: please don't make my mistakes.
The reason I lost coins is because I was tempted by Mt. Gox. Their 2FA auth made it seem very unlikely that my coins could go anywhere, just like Coinbase. If I'd researched Mt. Gox, I would have discovered a history of technical problems. Yet if you research Coinbase right now, you'll discover they've had a history of those too. There have been at least two or three high-profile Coinbase incidents over the years which were featured on HN. And if you research Bitstamp, you'll see they just lost $5 million.
The common denominator is that exchanges and webwallets aren't trustworthy.
No it doesn't. History proves the polar opposite; MtGox alone ate more coins (>750k) than all known incidents of wallet theft together.
Best practice is to use your own wallet. Has always been this way, will likely stay this way for a long time to come.
But sticking your coins into a webwallet like Coinbase without multisig control is a recipe for unmitigated personal disaster. A mental exercise is useful: "I've lost all my money." How would that affect your life?
I strongly disagree with anyone who would push the view that it's okay to sweep the issues under the rug in the name of making Bitcoin more popular. Putting people's fortunes at risk is almost equivalent to putting their lives at risk, because your quality of life is directly proportional to your fortune.
If Bitcoin sounds risky, that's because it is. No amount of regulated exchanges will change that. What will change it is giving consumers multisig control over their coins, or insuring against a total loss of all coins including cold storage.
There's literally no other option. One of those two things must happen, or you must not use the services. Or if you do use them, don't put in more than a quarter of what you're comfortable with losing. If that's $100, then never deposit more than $25 in BTC.
Remember, Bitstamp just lost $5 million USD to hackers, or half their most recent investment round. It's unknown whether they're currently insolvent. Everyone thinks they might have enough money to cover the losses, but nobody knows for sure. They could currently be a fractional reserve.
So Mt. Gox wasn't a one-off. Nobody is safe from hackers, technical issues, or even rogue employees that want to become millionaires. Due to the untraceable nature of Bitcoin, all exchanges and webwallets are extremely attractive targets.