... by the way, I am contemplating about a season this time without the titled players who found it not necessary to fight in our team even a single time, despite all my appeals. What do you think about this idea?

My idea would be to still let everybody take part in the season but only pay out rewards to players which have participated for "The Blockchain Chess Team" in at least half of the League encounters (where "participation" could mean to have played at least 8 games - which should be always doable).

To give everybody a fair chance you might start to count the number of participations from now on, so that nobody could say they hadn't known about the new 'rule'.

But this suggestion is only kind of "thinking loudly", and as you are offering the tournaments you should make the final decision and do things as you feel most comfortable with.