Real madrid is quite aware of Luca modric age and would probably not expect much from him as it was in the previous season. Modric already offered to Madrid all he could and I think Madrid is trying to reciprocate the good gesture by giving him the captain role. Luca even before now has been displaying leadership qualities in that squad and I believe he can do more better as a captain. Some of these young players need someone who’s capable of putting the squad together in and out of the pitch. They will surely listen and respect him as the senior player he is and as the legend.
Only he remains at Real Madrid as a veteran player besides Carvajal, at the age of 38 Real Madrid still gave him a contract even though at his age he should have returned to play for his first club (Dinamo Zagreb) or at least go to the SPL. Both sides show their loyalty to each other, with Modric at Real Madrid, it's hoped that the young players there can learn more from him.
BTW, have you heard about Los Galacticos 3.0? they say that Real Madrid is currently the third golden generation after the Zidane era, the BBC era.
In all games combined, his minutes do not mount to 25 games total, and this is a team that played like 50-60 games a season, so he did not play enough minutes to be even half of their games. He comes in very late, like after 80th minute, to make some changes, and try to see if he can give them a win or at least keep the midfield intact. That's all they do with him nowadays because he would be super tired if he kept trying to play with everyone else. On top of that, they need to give minutes to many young midfielders to get them some experience, if Modric keeps playing, even if he could, then it would not be easy for the younger players to get any attention and experience.
This is why I believe that they are seeing this situation as something that they could use him for only important moments for like 10-20 minutes a game at most, and not even that if the game is not in danger. He is not there to play, he is there to share his wisdom with the midfield guys at the team. That way, those young guys will have some leadership they can look up to, and they could learn from him and they could get a lot better in the process because Modric is there to help them. This worths another year of contract.