It appears that it has begun already. I speculate that Bittrex is moving in advance and preparing itself to avoid regulatory problems. I reckon next requirement from you would be your assets information and annual income. If you do not meet a certain level of income, they might limit your account.
This might become the standard requirement for all exchanges.
Based on the state of their support, and the fact that I was already fully kyc'd I'd say it feels more like they are getting ready to go full mt.gox than anything else. They literally don't have a phone number listed anywhere, only support option is to open a ticket that gets ignored.