You are given an opportunity to trade and in return they ask you to abide by the necessary security rules. What's the difficulty in just following these rules? This is your assets, so give some attention to your personal security. If there is any concern, that something might make any harm to you, the administration warnes you.
You mentioned a deposit of the coins which are alien to blockchain, and point out to Binance as an example. If you are so rich that you even don't bother to prove the wallet status and check the payment details, then make an experiment. Try to make a deposit in coins which do not belong to a given blockchain (not tokens into tokens), and then wait and see, how they will resolve this situation there.