This is a good way to control unwanted money (laundering money or terrorist finance).
but how can they identify and not to hit the bitcoin privacy of the bitcoin users?
This thing would be the big question because if they tend to engage into bitcoin because of money laundering and terrorist finance they would definitely hit up the anonymity features of bitcoin and we all know that tracing its users would really hard thing to do and thats the main problem that EU would face.
Money laundry and hunting down money streams leading to the financing of terrorism, are just excuses that governments hide themselves behind. It's once again their hunger for control that is leading to all kinds of ridiculous policies. Bitcoin is getting bigger with the year, and so does the wealth of people holding Bitcoin. It's the pure smell of money that is making them want to know who you are, and what you hold. Because if they know, you can't avoid the point where you have to pay tax over what you hold, the profits that you have made, etc.
I cant be sure but maybe this thing would be the main motive on this kind of plan of EU.You are right bitcoin is growing everyday and they can already see that people will surely put or hide their tons of money into bitcoin just to evade the taxes thats why they are clinging or imposing such laws or actions that would do against on bitcoins anonymity but i could say it will be a hard step for them.