Depends on the movie, as to the degree of divergence, but I certainly get your point.
The only part that is required to fill in the role is a character who starts off in Iron Man's camp, then switches sides to Captain America. Pretty much anybody can do that.
If they are going to go that route, and not have Spidey meet any of the expectations of him set by the comic, why even have him in the movie? At least having him fulfill the first action Spidey really takes in the Civil War comics gives the audience something they can relate to on an emotional level, since his character is so well known.
In the clip about Black Panther that was posted above, the guys on that show were talking about how this doesn't need to be another Spider-Man origin story, and that, to me, shows that they don't understand anything about Civil War. It was never an origin story for Spider-Man, it fully depended upon the audience already knowing about Spider-Man and his relationships. The Civil War movie can do the exact same thing with Spidey, because everyone already knows his story. They are already losing some of the initial emotional appeal by apparently removing the Stamford Incident from the story line (unless Winter Soldier somehow "causes" it in a similar way to the New Warriors). Having Spidey just put in a cameo or two, rather than using his character to connect the audience with the enormity of the decision he has to make just takes away another powerful dimension that the movie could have. Maybe if the Black Panther movie came first, and they gave us something to care about in the character, he could take on that role. I just don't see it happening at this point.