It is true that whatever you put into an exchange or something like coinbase in some perspective your coins are 'no longer yours' as they are out of your control. You no longer have the private keys nor any control of that amount in the exchange and if the exchange randomly disappears or decides to disable their wallet like Poloniex then all your crypto is gone.

That is why it is always good to use a hard wallet or a paper wallet rather than keeping your money in an exchange. Trezor is a great one to use.

You may think it will save you time if you don't have to transfer between your wallet and an exchange and that if you have invested in multiple coins it is easier just to leave it in one place, however, with the recent freeze in bitcoin trading it is best to get your money out.

Hopefully this post will save some peoples crypto @stellabelle! :)