I don't believe that we have had what us older Rangers Fans would refer to as Captain material for a number of years. Certainly Tavernier is as good as any that have preceded him since the departure of Walter Smith and what followed. It could be argued that McGregor would do a better job but then we have the arguments of whether goalkeepers make the best captains, and yes Klos didn't do too bad in his day.
For me, until we have a born leader in the team and so long as we hold on to Tav, he should stay as captain.
Of the players currently at the club, some of our young players could have the potential to lead the team. Rossiter showed with England Under 21's that he has the qualities but right now there is no guarantee that he can stay fit or indeed secure his place in the team. McCrorie again is a youngster that might have potential as a future captain but again he is young and finding it difficult to secure his position in the team.
Leaders are born that way. It is the same in any industry and football is no different. You only need to look at Souness, Gough, and Gerrard himself to see that.