I found it interesting that the episode painted Tony as such a staunch opponent of superhero registration, the opposite of his position in Civil War. I was kind of expecting something to happen here that would change his mind, but he was still against it at the end. Maybe that's because Cap being a Skrull impostor pre-empts his role in the CW story.
I think EMH's portray's this Tony as someone that values being part of a team.
To register would mean going into the private lives of his team.