This is all fine, but it also needs to be a player who's capable of being on the ice in the most important moments of the game. If you wouldn't want a player on the ice in the final minute of the SCF, they should not be considered to be a captain.
There's off-ice leadership, and then there's on-ice leadership.
Mark Borowiecki and Ron Hainsey, for example, might be great guys off the ice, but believe me, if they're not pulling their weight in important games, other guys will tune them out real quick.
A leader doesn't need to be the loudest voice or biggest personality in the room. Look at what Kawhi did last season with the Raptors. He probably said two sentences in 8 weeks, but that entire team changed because of the example he set on the floor.