Aren't they one of the last non-KYC exchanges left, or have they done away with that?
I think they are still among the rare centralized exchanges without mandatory KYC. Unless you are US resident.
KYC is now mandatory on Mexc since June 30, 2024.
https://www.reddit.com/r/MEXC_official/comments/1c5j52k/mexc_requiring_kyc_for_triggered_users_or_all/https://medium.com/coinmonks/first-binance-then-kucoin-now-mexc-is-going-full-kyc-your-best-alternative-755c4bbcb48d#:~:text=MEXC%2C%20a%20rising%20star%20in,so%20will%20restrict%20account%20functions.
There are basic/primary and advanced verification on Mexc.
This is the primary verification on my account on Mexc which I have not gone for:

Instill see withdrawal limit of 10 BTC on my unverified account but I do not send any coins to Mexc again since June 30 because I am not ready to get verified for now on the exchange.
They exchange is not also available to residents in Samoa, Bermuda, China, Cuba, Cyprus, Egypt, Iran, North Korea, Malta, Singapore, South Sudan, Syria, Virgin Islands, United States of America and Venezuela.