Some exchanges are even dubious such that they will increase the difficulty of the KYC when they notice you have already deposited. This is an attempt to confiscate your fund. So, it is advisable to complete KYC before using an exchange.
what happens is exchanges do not ask for KYC because there is not a global regulation and when the became big they change terms of use change, so all Whoever deposits using old addresses that he used will fall into this problem, and sometimes even after this happens, good platforms provide the option to withdraw without being able to perform any other action like trading. I repeat, if they do not ask for identity verification when depositing, they are scammers.
If you believe that someone will be doing something illegal for you, and not to you that means that you are gullible. I believe that anyone who is willing to do something so illegal, should realize that you are not going to end up with anything better in the end, and shouldn't really get anything done. It's just that simple and we should be making sure that we deal with a KYC place if we pick an exchange.