It is true that whatever you put into an exchange is no longer yours. 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.

You may think it will save you time if you don't have to transfer between your wallet and exchange and that if you have invested in multiple coins it is easier just to leave it in one place, however, most of the time things don't last forever and if an exchange disappears then RIP your crypto.

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