I always don't see any reason why a trader should be fearful of doing KYC on a well known legitimate exchange once the source of the funds you're moving to the exchange is from a legit source and also being used for legitimate activities and businesses.
One important reason to avoid KYC is that corporations lose data in huge amounts, and the attackers who acquire it can cause very significant trouble. This is a waste of time, money and nerves.
If you look at
the biggest corporate data breaches reported by Wikipedia, you can see that most of these corporations are not held accountable enough, and some lose data more than once. And exchanges collect enough information for KYC to go through a similar procedure in so many places. And accounting data from exchanges leak regularly.
If we take into account only the monetary part of the losses,
according to Britannica, in 2021 in the United States alone, 42 million people became victims of identity theft, which is 12.5% of all residents of the country, including infants. Total losses for that 2021 alone from identity theft amounted to $52 billion.
Of course, it is up to you to decide, but there are reasons for a respectable person not to undergo the KYC procedure.