I very strongily disagree with you.
The captain very much has a role on the pitch, a captain is the one who sets the tone, who leads and when the chips are down either by force or by example forces those around him to raise their game in a way someone stood on the sidelines can't.
Think of the way Keane used to inspire his Man Utd side, of the way Viera would fight for the team and inspire those around him to fight, look at the way Gallas sat on the turf at Birmingham and Arsenal's season collapsed around them. Look at Terry playing for England in Germany last month.
The captains role is vital.
Couldn't agree more. Keane in the tunnel with Viera after his comments on Neville was exactly what you wanted from him at that point. Protecting "his" flock from the outside.
Also I know from playing cricket if my captain starts getting pumped, tearing after balls through the in-field or giving a bit of banter to the batsmen, we all seem to follow and work together.
Captains are there to unite people on the pitch. If the team is losing grip on the 50/50's I think a good crunching tackle by the captain soon sorts that out. There is a lot more to a captain than just it's status. For example you wouldn't make Nicky Shorey captain would you? it would be Friedel, Barry, Reo-Coker or Laursen, maybe Davies. But mostly you look for someone who can fit the role of Captain. Therefore it must have a purpose.