I agree with you that Luka Modric loves the club Real Madrid. For this reason he is sign a new contract with Real Madrid. At this moment, I think real madrid club needs an experienced player like Luka Modrich. Because Real madrid squad have lack of experienced player right now. Real madrid have a lot of talented player there is no doubt. But in Madrid squade there is no experienced player.
In midfield, Madrid have some talented player like Bellingham, Camavinga, Valverde and Tchouameni. Every player are very talend. But they are not experienced like Modrich or Toni Kross. Thoug Toni Kross is decide to retirement, so now Madrid now needs Luka Modrich. If Toni Kross did not the decision to retirement, I think then Madrid management will not sign a new contract with Modric. However, Luka Modric is a living-legend of Madrid team. With the help of Ancelotti and Modric, Madrid's midfield will play more better in the next season.
I believe with Madrid's management keep extend him one year contract is very good decision, Madrid need senior players would be guide for young players and this season have more dominance exactly after leaving by Toni Kroos. Seems interested with Luka Modric fight won't retired regarding some players on his age almost over for playing with the top European team.