Your bitcoins should only be stored in cold storage wallets after purchase, and transferred out when you want to sell them. It takes less than 10 minutes. Remember, if you don't have the keys, it's not your coins.
Deliberately bold the sentence above because it is a truth. Ironically to date nothing will stop people from having their assets in exchanges. They decide whatever they want including save their funds on the exchange.
The last thing is, regret will come too late even if now everything seems safe. There are many exchange hacking incidents, it is the most feared thing but actually it also doesn't prevent people's interest from having funds in exchange. This solution is for those who care about the safety of their funds in the long term so they don't care about the fee incurred to transfer assets to a personal wallet.