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I think nowadays many people doesn't care about their privacy anymore. In the case of bybit banning users, it will be better if they gave some early warnings first for each of their users because it's too unprofessional if they will just ban them immediately.
Yes, an exchange where KYC verification is required should ask for documents as soon as the account is created so that the user could not even make a deposit without verification and doesn't get his funds stuck.
In this sense, the binance is good as they don't allow the user to make deposits without KYC verification.