KYC is implemented by crypto exchange because they are required to do so by the government and it's done to prevent scams and money laundering according to the reason they stated about the need for KYC. If you are giving out your details for KYC purpose it should be to a reputable exchange, that will reduce the risk of your details being used for scam purpose. Should you fear about your details going into the wrong hands, yes, but it can also go into the hands of the government authority that can investigate you if there's any problem that was traced to you. If you want to avoid KYC on centralized exchange, there are some that allows you to transact freely without requesting for KYC unless you make deposit that was above your account limit.
The primary reason why centralized exchanges requires our KYC is because of government regulations, I might be wrong but I believe that some of them might not be too interested if it is laundered funds that is going through them. Their mindsets could be that they're just a channel to trade cryptocurrency and governments should worry about catching criminals but they don't have a choice but to comply with regulations. Think about it many businesses don't care how you got your money, they are more concerned about giving you their best services and getting paid. I don't mind completing KYC requirements in CEX and banks, it is a necessity to avoid crime, the requirements have been able to reduce money laundering for drug and terrorism. We the customers don't need to like the KYC process but it is for the better good of all to minimize crime.