There are a few problems here.
The primary being the current running of S.H.I.E.L.D. Because of the corruption, this could really have the shit hit the fan.
However, the flip side to this is that you have people with unbelievable power running around being vigilantes.
While Spider-Man makes good points, I can't disagree with this agenda. I think what pushed Cap over wasn't so much the Initiative, but making a task force to take the people who don't sign on down. That's pitting friend against friend, and Cap wasn't about to hunt down, say, Peter just to sate S.H.I.E.L.D's latest ego-trip.
But even then...I can't help but agree with IM here. The argument is simple: The Constitution gives you the right to bear arms, but not any dickhead can run around with guns; there are rules. What's more, you can even LOSE the RIGHT to bear arms. These people have rediculous power, only it's inate. What accountability do they have? Do they have any training? I mean, what happened with Speedball's group was a perfect example.
While Logan may have problems with this (understandably)...I can't help but agree that people with that much power simply must have some kind of training. If there were a way to register them, employ them, but keep it on the DL (perhaps making their identities Highly Sensitive and Classified information? akin to CIA Identities) then I cannot see why you wouldn't do this.