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.
And what's good in providing all your personal data for any kind of actions? Maybe the fact that you will pay fees for each of your transactions? I prefer to remain as far from the govt as possible. That's why I prefer no KYC in everything: starting from exchanges and ending with messengers.
Well, it's not a secret for anyone for a long time. All personal data that is collected is then used for the profit of the company and/or for the purpose of control/surveillance, etc. I would not like to seem like a supporter of conspiracy theories, but I think that the information on the Internet about this is enough.