It would be *great* if you could run the Bitcoin full node because Bitcoin really needs more of them.
if you are using coinbase just because you dont own a computer, i think it is better to use paper wallet or blockchain.info wallet for you to have full control over your private keys and coins and your money will be much safer than trusting a 3rd party site coz they can be shutdown in rare cases
Coinbase has to do that though. Read through their insurance they have for overall if they gave private key's it would be easier to possibly lose coins. It's meant to be new person friendly.
And if website has a hack, not one user getting hacked but truly the website/company caused it then it should be insured. It's never been tested so you never know but they hold a insurance most dont.
Yes having private key is great, but make sure cold storage if counting on this. Getting paper wallet off blockchain.info is not really a cold wallet as it's also online.