It depends what your goal is. Normally when sites have a user’s key encrypted as to be unreadable to the site, it’s to have a system where users don’t have to trust the site not to steal the key. In that case, then no, because the whole point of a technique like that is to have it so the service provider doesn’t have control of the user’s keys at all. Any workaround to that would defeat the purpose.
If your goal is to protect the keys from outside hackers, then the site can (and most do) employ cold storage or hardware security modules (basically a fancy hardware wallet) that store the keys. In this case, the site owners still have full control of the keys, and the users have to trust the site owners to be honest. However, the scope of a potential hack is limited, as the keys are stored either on dedicated hardware, or if in cold storage, large withdrawals are performed manually by site staff after review.