The chief problem with Civil War is that it's pretty much a well established cause=effect issue that registration=super-hero genocide in the Marvel Universe. The Mutant Registration Act (the previous incarnation of the SHRA from Civil War) was a massive plot device in the X-Men books about it being one of the inciting events/fixed points in history in all of the timelines where the Sentinels enslave the planet and kill all super powered beings, mutants in particular. If registration happens? Then you're fucked because Sentinels are coming no matter what you say and do, with relations to registration being the first domino to fall that leads to ruin and carnage.
Furthermore, it goes against Iron Man and Reed Richards' own established histories that they would bend over and spread their asscheeks like they did. Stark is a known contrarian who has ragequit the Avengers for less and has a long history of refusing to be made the government's bitch (to the point of threatening full-on war with SHIELD at one point over them trying a hostile take-over of Stark's business to get his Iron Man tech). Not to mention Reed himself personally KILLING the Mutant Registration Act by going before Congress and telling them point blank how exceptional the idea was and how registering ALL known super-heroes would be an endless headache even IF people agreed to do so back in the Walt Simonson run of Fantastic Four.
It was a classic example of Millar basically throwing out all known characteristics to tell a story he wanted to tell (damn the actual reader), complete with him causing irrevocably damage to Iron Man and Captain America by literally recasting them as Batman vs Superman, in terms of taking two characters who have minor scraps in the past but who ultimately would do anything for the other, and turning them into Batman and Superman clones that secretly hate the other's guts and would betray them in a heartbeat if they could get away with it.
HA HA HA HA HA HA HA HA HA!!!!!!!!!!!!!!!
Did you actually READ Secret Invasion?
Not only did they NOT use Skrulls to fix Civil War (or Avengers Disassembled, or any of the other stories in the lead-up to Civil War fans hated) but they fucking went out of their way to ATTACK fans who were begging them to use Skrulls to fix the shit they broke to spite fans! Right down to having Bendis outright have the Skrulls watching the lead-up to Civil War and saying point blank "pass the popcorn!" and ordering the Skrulls to stand down and let the carnage play out without taking a side so they could let their enemies destroy themselves, at which point they then started their 50 State Initiative infiltration.
Fuck, the only character Civil War "fixed" was Hank Pym via absolving him of all culpability in Civil War via being revealed to have been replaced by a Skrull prior to it and even that was done because Marvel finally broke and needed a containment book for fans who hated what Bendis was doing to the Avengers, given how much damage Bendis and Civil War did to the franchise and Marvel in general.