If Tony isn't in the movie, it's a less interesting story, but the story fundamentally still works. Ross presents the accords, Cap rebels, some side with him, some don't, there's a chase for Bucky, etc.
There is no story here without Cap though. Cap is the one who adds conflict. In a Civil War with Tony and without Cap, the accords are presented, Tony and co. sign, nobody gives a shit about Bucky, and Zemo's plan doesn't have any fight to exacerbate. Cap is the major point of resistance to the accords, the biggest driver in protecting Bucky, and the reason why there's a civil war at all.
A more faithful adaptation means including *more*, not less, of the comic. Which would include the things that readers hated. Changing the story to get rid of that stuff would mean a less faithful adaptation.