But I did: if you read my comment you will see I literally wrote that you don't have to store the wallet yourself, just use some online wallet. Another option is a hardware wallet like Trezor.
What I don't understand is why would anyone who is so scared of using Bitcoin transfer money to Coinbase to buy Bitcoins. To me this is the same as withdrawing all your money from your bank while being super scared of having your own savings in cash at home.
To buying bitcoins on Coinbase (and almost any other exchange) one have to use their online wallet. Fear was not a decisive issue when you (fig.) decided to buy bitcoins, but for whatever reason it is now that you want to move them somewhere else?
What I don't understand is why would anyone who is so scared of using Bitcoin transfer money to Coinbase to buy Bitcoins. To me this is the same as withdrawing all your money from your bank while being super scared of having your own savings in cash at home.