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OK, I will go through the KYC procedure, and what will happen to my anonymity? All data about the user will be known, and anonymity is something that is very appreciated.
It is assumed that if you completed KYC in any company, then this data will remain there only. Presumably, they do not disclose information about their users to third parties. Thus, you remain anonymous, for example, on any exchange. But in practice, there is some risk of information leakage with data about you. So, the best anonymity is the absence of KYC.
The problem is that there is no security of personal data, very often hackers steal the personal data of users.