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Exactly - great answer. This is crazy - you create a private key then give it an 'exchange', who is not regulated, whom you have no idea of their security, policies, structure - probably set up in the 'goldrush' as few years ago and people wonder why?
Your private key is private - it is not meant to be shared with anyone, not even an exchange. An exchange should be able to facilitate a request but not have access to you private key. If an exchange knows your private key then why bother with keys? Why not let the exchange just provide you with an ID that they have created?
If you have to give your private key away in order to get your money then there is something very wrong with the process...