Except that they already explained this in the comics, and making Parker sign was a bit of an oversight. He lives in a world wherein some of the biggest villains are those who can access information. It would take very little time, and some surveillance, to eventually find out who was under the spider costume. That's not to say he couldn't be protected by shield, but he now has to keep his family and friends out of trouble...everyone he meets and befriends is a possible target.
In general war is never ending, so it doesn't matter if you're registered or not, bad men, will still continue to burn the world. If a villain with say; the strength of Superman(Hyperion for accuracy purposes) felt like leveling a city, you wouldn't know it till it was too late. For me, leashing power only comes from those willing to wear the collar.
