Your question assumes money custodians behave in an honest fashion.
An honest bank or exchange would simply keep your coins stored safely for you. But many places aren't honest, and make their money not from the transaction fees but by lending out the coins you've got stored there to someone else. As long as people don't all ask for their coins back at the same time, this works great for them. Your coins will be entered into some investment scheme, to make them return a percentage rather than just sitting there doing 'nothing'.
One does have to be careful however not to lend out those coins to someone who just runs clean off with them, or invest them in some scam that accidentally tanked to zero. Otherwise that money they claim to hold may not exist any more, which causes a problem if the customers ever ask for their money back all at once.
An honest bank or exchange would simply keep your coins stored safely for you. But many places aren't honest, and make their money not from the transaction fees but by lending out the coins you've got stored there to someone else. As long as people don't all ask for their coins back at the same time, this works great for them. Your coins will be entered into some investment scheme, to make them return a percentage rather than just sitting there doing 'nothing'.
One does have to be careful however not to lend out those coins to someone who just runs clean off with them, or invest them in some scam that accidentally tanked to zero. Otherwise that money they claim to hold may not exist any more, which causes a problem if the customers ever ask for their money back all at once.