I agree we can't know for sure, but I think we can get a sense of who makes a good captain from what we see on the field. Maybe not.
I think that's an interesting question about what a good captain's main role is. I've always thought the ninety minutes on the field are the key, being able to deal with the referee, intimidate opponents, direct your own team. It's then that they can tip a game one way or another. I think veteran leaders off the field like CJ have a positive clubhouse influence whether or not they're captain. But perhaps that is underestimating the importance of officially being captain in the clubhouse.
Certainly all of the on-field things you list are very, very important roles of a good captain. But my personal opinion is that they are not any more, and maybe even less, important then what happens off the field. As I said more time is spent outside of a match then in it and if you have a captain that can create a positive influence in many different ways off the field then it's a logical assumption that you are getting MORE from your captain based on the amount of time that positive influence is being imposed upon the squad. Not to discount the in match effect that a captain has at all, only to say that outside of the match is also huge.
I use two main observations as my basis for drawing this conclusion. The first is as a coach. I've been coaching youth teams for about 11 years now. All of the travel teams that I've coached I've allowed the team to pick their own captains by voting. I can say with great confidence that the best captains, the ones that had the most positive influence on the team, were the captains that took their leadership role in practice, warm ups, while traveling etc very seriously. They created an environment where the other players were held accountable by their peers and not just their coach and this created a team that worked harder, smarter, better. I could go deeper in explaining this but really the point is that a team with a good off the field leader is going to be leaps and bounds better then the team that doesn't have a good off the field leader, no matter how strong the onfield leadership is, from my experience.
The other observation is as a Chelsea fan (cue loud groans). I am just constantly reading about the mostly positive and sometimes negative effect that John Terry has on the team as a whole. More often then not it is the spirt and motivation that he provides off the field that has made him such an admirable Captain. I'm sure there are many similiar examples throughout the world but that one is just mine.