I'm not familiar with the Civil War storyline firsthand, but from what I've heard of it, I can't see that sort of thing working at this point in the MCU. This world is too young and, as has been pointed out, has too few heroes. Also, SHIELD already knows who all of the major heroes are and keeps an eye on them to the best of their ability.
Maybe it could work at a much later phase when they've developed more properties. In the meantime, CA:TWS is clearly exploring the security vs. freedom issue in its own context.