"King of the Hill"

That's exactly what I mean. By the time it's your turn, you'll have forgotten that you even registered, the enthusiasm will be gone, and there won't be much incentive to keep going. But if we implement the system I suggested, no one will fall asleep – they'll have to keep submitting applications, and the intrigue will always be there. But of course, this is just empty talk; I'm sure the organizers have thought about it, but they decided to implement their own idea, which is closer to their heart.

As practice shows, even in regular tournaments, enthusiasm can fade. How many times have there been situations where people withdrew in the playoffs, in the round of 16 or the quarterfinals? Why should that bother me? It's stated in my first post that before each game, I will contact the selected player. If they are unresponsive, I will move on to the next player, and so on, until I find someone who still has the enthusiasm.

It will be interesting to have the most points compared to other players and watch as they gain points, while you can't do anything because of the randomness...

If you only select players who have already accumulated a certain number of points and ignore the rest, that would be much more unfair.
Randomness is great – let's hope for it and rely on it! :)

What's the point of trying when a certain group of players will have a lead in points (due to randomness) and, thanks to the randomness, have a greater chance? After 3-4 months of the tournament, you can just give up on the incentive to play against them.

There will always be something to strive for. I need players here who will play to win, not just to participate. They shouldn't be intimidated by the situation where one player has been in the lead for 2 months; they should try to beat him and stay in the lead for 3.
And remember that the tournament won't end in a year – it will continue cyclically (provided that interest in it doesn't wane), and the player who, for example, first plays in December, if they win, will start the next year as the King of the Hill.

The tournament will be tested for a while. Gradually, I will determine the optimal number of players (there should always be a limited number), and I may make some adjustments to the rules. But, as some have suggested, I will definitely not have multiple matches happening simultaneously, as this contradicts the very essence of King of the Hill.