Sorry but with current high cases identity theft where customer details later find their way into the dark web for resale. I don't think it's a good idea.
At least if it's a reputable exchange, people will have some little faith into doing KYC.
Do you ever use bank services?
The difference is that this is the web, Banks are in most cases regulated by Governments. Here on the web you just can't trust anyone. Any how with you details without ascertaining how good they are. You first have to prove yourself that you are a great exchange to work with.
Bank as an any other financial institution is regulated by government. So we are. As we are the financial services provider regulated by Financial Intelligence Unit of Estonian Ministry of Internal Affairs (FIU is a Police Department which regulates virtual currencies and forex exchanges). Our regulation is more strict than banks in several jurisdictions🤷🏻♂️ Believe me... for 3 months of operations we were called to their office twice to check our compliance with legislation.
And do not forget about the GDPR with it enormous fines for non compliant attitude to personal data...
The only thing to worry about regulations and identification process is the absence of anonymity. But in EU all crypto exchanges must be compliant with AML directives by 2020, so all will be regulated. And in USA even earlier I think