KYC exchanges are exchanges that guarantee the safety of their users, there may be some exchanges that do not use KYC, but as such these exchanges are less secure, and look un professional, I really like KYC exchanges because they are of good quality and professional.
Sorry, but I would doubt the first half of your statement a lot! Yes, reputable exchanges that are licensed and well established in the market are quite trustworthy when it comes to KYC. There are a loooot of exchanges asking for your documentation with nothing else in mind but selling your data on the black market. Don't take KYC as a an indicator for the trustworthiness of the exchange itself...