Well that's not entirely true. If the game wants to be in such level realistic, we should not be able to boost the morale of the players with 2 taps... (What a spacialist is this who boosts so easily your morale, I want him too)

For me captain could play a role in the morale of other players of the team.
Captains are influential, thats why thay are selected.

Good selection of a captain could slighlty improve the morale of the team or/and make it harder to drop down..

Now which parameters would make a good cap is up to the devs.
Age, matches played or a new skill... influence could be introduced.

These tiny details make a good game better.