I have only verified my ID on Binance, since I 'trust' them. I pay my taxes so I have nothing to hide.
I do not trust Binance,,, but among all the exchanges that I can access to, I believe this is the least likely to defraud me. It is not that I have hundreds of dollars in exchanges anyway but yes, like you, I generally do not mind KYC for stuff like Binance. I got nothing to hide either,,, just that I really hate exposing my confidential information online.