Because KYC procedure links wallets with the actual user’s identity it can lead to information leaks. A recent study concluded (
http://stevengoldfeder.com/papers/ZKCSP.pdf) that 53 out of 130 platforms the research was conducted on leaked critical personal information to a total of at least 40 separate third parties. The absence of enforcing KYC does not affect the user's asset security on the platform whatsoever, and furthermore protects the user as information leaks can lead to serious issues such as identity theft and other fraudulent acts.
Mt Gox is the most notoriously 2 x hacked crypto exchange which enforced, rather still enforces KYC/AML, and while it helped them trace some of the lost funds it still managed to lose them in the first place and was the most prevalent exchange of its time.
I personally prefer no KYC.
Prime XBT (
https://primeXBT.com) can be added to the list of trading platforms that does not require its users to submit to the KYC procedure.