I think KYC helps exchanges to control and track their users to avoid cases of scam or money laundering...The exchange collapse issue has nothing to do with KYC. The collapse of exchanges has legal implications and the government must be held responsible. But another thing is that we don't want to be controlled by the government, we want to be free, but when we are scammed, we ask the government to solve it. This is one of the loopholes in the crypot market and scammers are fully exploiting it.
The only way users can scam an exchange is if they can hack it, aside from that I don't see any possibility. KYC is just a simple verification process where an exchange would like to know their users and it's mandatory to all legal exchange as they are regulated by a certain agency of the government, so there's no need to question that because exchanges nowadays are like banks.
If we are expecting full anonymity, then there's always this decentralized exchange, but the problem is they don't have the volume like CEX, and that only tells us that more people trust centralized exchange over decentralized exchange which we can conclude that most of them do comply with the KYC.