If this is really enforced in the form as wished, then many will go for anonymous alternatives. Monero, Dash, ZCash etc. In the end, it will be a cat-and-mouse game where users will always win. The good thing about this technology is that you can never really control it. The technograts in Brussels, Washington and elsewhere in the world will yet have to learn this.
The European Union Wants to Identify Bitcoin UsersThe European Parliament and the Council of the European Union have proposed amending a directive on preventing money laundering and terrorist financing that will require cryptocurrency exchanges and wallets to identify suspicious activity, a directive that would include identifying bitcoin users.
https://www.cryptocoinsnews.com/the-european-union-wants-to-identify-bitcoin-users/ Same as US government, IRS, and all governments and banks. They want to know how you spend, where are the money flow, and all details. For bitcoin it will not be that easy, but if they issue their own cybercurrency, they can do that.