If it was The Avengers Initiative, being run by The Avengers, and not the government, then yes, i would be for it.  But we live in an age where government laptops containing the social security numbers of soldiers fighting overseas are lost or stolen rather easily. 

If it was being run by Tony Stark, there would have been no Civil War.  But it was a governmental mandate which made it unpalatable.

The X-Men teams have been "registered" for years, with the leadership knowing who and accounting for all those who fought under their banner.  Same with the Avengers.  At least 3 of the New Warriors were reserve Avengers for crying out loud, so there was already a de facto registration without governmental interference and oversight.  All they had to do was create some sort of "Junior Avengers" program run out of the Avengers' Mansion via one of the old Hulkbuster bases in Arizona or Nevada.

But ya know what? Stamford would still have happened, because Speedball/Penance did not do enough to make sure the battle was contained away from civilians.  The only difference would have been that maybe, just maybe, a few more heroes would have died.