I can use myself as an example back then I was still new in this space I usually store or should I say hold my tokens in Cex wallet until , I found this forum , I now began to see the beauty of privacy.
Storing in cold storage doesn't have to do with privacy, but with security.
So, buying from a CEX, using KYC and then sending to a cold wallet, doesn't erase history. This means that there is a submitted transaction in the audit records, where you (the real you) used X amount of dollars to buy Y amount of BTC and then withdrawed this amount.
My opinion is that if you choose to follow the pattern above, there is nothing wrong. Just be aware that there is no "privacy" in this.
For me the problems start for people who buy
and hold BTC on CEXs. Because this can be proven devastating in case the CEX decides to prohibit withdrawals. Essentially you have a false idea of "owning BTC" where in fact you "give your BTC to a CEX to hold it for you".
So to summarize:
1. Buying with CEX and holding BTC there:
BAD security,
BAD privacy
2. Buying with CEX and holding in your own wallet:
GOOD security,
BAD privacy
3. Buying P2P and holding in your own wallet:
GOOD security,
GOOD privacy
However, even if you do the (3), there is nothing to guarrantee you that you 'll be perfectly secure and private. You just increase your levels of security and privacy expotentially.
Now, finally, if you ever wanna choose from the 3 options above and you can't do (3), please never consider even for a second to choose option (1) instead of (2).
Keep this mentality and you will be good:
Money in CEXs can just be considered lost money and if you are lucky, you may get them back in the future.