I'm a foreigner to this country and have been for over a decade. They already track our details and you are required to fill in enough information on the landing cards each time you cross a border that allows them enough detail to track you down. For all you out there talking about sinister plots, the data is already there in their hands.
Here's something for you to consider.... We are about to embark on a process of negotiation around Brexit. Why shouldn't the government know the costs associated with educating EU citizens when a huge exercise around how much money should be moved around EU and UK expenditures is coming up? I think it's legitimate personally for the negotiators to know how much cost we will be left with to continue to educate students of EU citizens who are allowed to remain. The EC are very shortly going to throw the British pensioners living on the continent into the frying pan when it comes to how much it costs to access services in the EU post Brexit. These are all costs that need to be known for Brexit to be fair for taxpayers on both sides.