Kuroo's entire character, from the very beginning, had ALWAYS revolved around his love for volleyball. His entire backstory was about that, the reason he grew out of his shyness was because of volleyball. This boy wanted to play the sport every chance he gets.

Here's where his love for volleyball differs from people like Hinata or Oikawa. Kuroo loves the sport, but he also truly wants other people to understand that feeling, to love it as much as he does. We can see this with how he dragged Kenma into it, and taught Tsukki to have fun.

Kuroo has a lot of amazing character depth, but he doesn't actually have much character development* OUTSIDE of that backstory of him and Kenma as kids. He had his development prior to Haikyuu. Instead, he became someone that plays a role in aiding other characters' developments.

We can also see that his motivations for improving was always to be able to continue playing, to fulfil his coach's wishes before he retires, to just feel good about winning for himself and for others, as a team. But it was never about being the best at it unlike Hinata, Hoshiumi

Kageyama, Oikawa, and everyone else who did end up becoming a pro. So Kuroo being someone who essentially promotes volleyball, is the perfect summary for his character. Now he gets to show the entire nation, even the world, just how amazing volleyball is.