Ironic isn't it? The most useful service and (... no seeds, no stems, no sticks))) nobody knows nothing about the way they operate. They gotta use something to generate btc wallet addresses for the registered users aren't they?
Before you go in the direction that no one knows anything about their business, a few minutes of searching on Google would give you enough answers to change your mind. Coinbase is not some secret agency, but it is also not a completely open organization that is required by law to share all information with the public. I may be wrong, but only Coinbase described in detail the process of generating private keys, which some didn't like because they thought it was a security risk. I don't believe any other crypto exchange has more security then Coinbase, but that doesn't mean people need to keep their funds there.
Why You Need a Physical Vault to Secure a Virtual Currencyy2k-2016, do you feel better after reading the article?