Board Game Arena

Why not have tournaments for this game I see no reason but please let me know if I’m wrong

Because it's a cooperative game?

Can't you just do the Swiss system?

While Hanabi is a cooperative game, you can play tournaments and competitively by looking at things like speed, game score and overall team skill with regards to avoiding risks of having an important card be at the bottom of the deck if there's a way of playing set seeds.