No they won’t, no more than they have to now. of course more importantly if you’ve got a bitcoin card that they’ve associated with you and you meet some guy in an alley and pay him with that bitcoin that they know to be monitoring and you guys hit the internet via your smartphone to transfer money you just told them where you are. Better than turning you off, you’ve now got a tracer.
I was thinking more along the lines of not some kind of “card” that you would run through a terminal to spend (which you could do and draw on some Bitcoin account) — but rather keeping all that information offline, and in a small storage device that that you have with you.
Just think of it in the same manner as dealing with cash with someone else (except “cash” no longer exists at that time). Now, it’s possible with “cash” to track down people, but it’s difficult and it’s possible to “stay a step ahead”.
And if push comes to shove people are going to do it.