So it appears that most of the people are Team Cap, mainly due to the fact of "government registration" when the entire movie and all the crap was directly caused by Cap being arrogant and thinking he's above the law. If he just went along and they brought Bucky in it all would have been solved rather easily without wonton destruction.
They planned to kill Bucky at first. So yes most of the problems would have been avoided if Cap had let the German special forces kill Bucky. Of course then Zemo would still have been around and made another plan.
But here's the thing in the real world Iron Man and UN is clearly correct, the Avengers are fundamental a paramilitary group with weapons of mass destruction and no oversight, funded by an American billionaire.
The problem is that when we see it in the context of the movie universe Captain America may be right. Let's look what would have happened if the Avengers had followed the government.
First Avengers: Captain America would have continued to be a entertainer and Red Skull woulkd have destroyed all major cities in the world.
Avengers: New York would have been nuked
Winter Soldier: Hydra would have won.
Of course Iron Man movies show the entirely opposite history, Avengers is the the only movie where he fight a problem, he or his father hasn't created. It's why the movie function so effective, all the other stories have serve to set up why the character act and think the way they do.