The best way to keep your bitcoins safe, is to use a hardware wallet that have stronger cryptography that web wallets.
If you store your coins in exchanges you are most likely to lose them, because exchanges receive the most cyber attacks.
You have a point about that. It is really hard to store your coins in the exchange wallet because it is prone in hackings and some computer virus that can steal your money. Internet is not really safe for our money and that is true. So, if you have an alternative idea or ways to secure your money do it as much as possible. So it will be safe and secured.