Leadership and skill are two separate things. Often teams appoint their most talented player as captain, regardless of leadership ability, but I have always felt that is a mistake. Sometimes you get lucky and have someone who is both talented and has leadership qualities (Crosby, Messier, et al). Someone can be an on-ice and locker room leader and be a 3rd line or 3rd pair player. It also seems that someone with lesser ability, but outsized work ethic, can make for an excellent leader.
I seem to recall someone involved with the team saying that Staal, with all the significant injuries he has suffered, has been an inspiration to the team's younger players. Leadership comes in all styles, and by any stretch, Staal qualifies. He might not be a "rah-rah" leader, but then neither is McD or Nash. Stepan was not a rah-rah leader, but was most definitely a team leader. The last rah-rah leader we had was Callahan.
By having 3 alternate captains, the Rangers are also covered if Staal ends up as the 7th D.
So, when it comes to Staal's leadership role on the team: remember that he is looked up to for his work ethic, dedication, experience, and career accomplishments. He merits the A.