There are cold and hot wallets. Because of hacks in the past and development of technology, exchanges and platforms change from hot wallet to cold wallet for safety of their funds.

So when customers make deposit to a hot wallet, a platform will move it to their cold wallet, and credit a number to customer account. Later when that customer submit a withdrawal request, that platform will approve (or disaprove) that request, and send a number of coins requested to withdrawal address of that user.

Number of coins stored in hot wallet is not big and platforms nowadays store most of their funds in their cold wallets.

Many wallet addresses in rich list is cold wallets: https://bitinfocharts.com/top-100-richest-bitcoin-addresses.html