Yes I'm scared if I lost everything I hold into it that's why when I'm storing my coins into wallet I always look for the private key so that I can be able to access it anytime in it's supported wallets and also I am the only one responsible for it's security as I have the only access into it by the use of private keys.
Even online wallets provide you private keys, you should know that you are not a single person who have private keys for your online wallets. Sites and owners of those sites own your private keys too. Consequently, what if they are bad guys and plan to steal your money? If they are, they plan, your money will be stolen.