Player rating for tournaments across all installments of Heroes.

That's true, and the opposite is also true... For example, in the third game, players consistently perform well from tournament to tournament, while in the second game, they don't - for various reasons... Players in the third game are gradually moving up. The others are standing still... In my opinion, a GENERAL CURRENT RATING is a utopia.

As the rating ages by 1/3, it's still unclear whether it's better to stand still or move forward. Those who play for the rating understand this perfectly; that's what makes them players. They crave the game to gain more rating, but they also understand that if they perform significantly worse compared to the previous tournament, their rating might decrease. It's a kind of hunt for luck.
If the rating ages by 1/10, then even with a very poor performance compared to the previous one, the rating will likely not decrease. You yourself pointed out one of the reasons why VGAP used a 1/3 reduction. And in general, it seems to be taken from real-life rating calculation formulas, perhaps from Elo or some other system; I'm not sure.

Added 4 minutes later

That's what I'm talking about... I don't think it's necessary to collect leave requests. This is an unjustified burden on the organizer...

That's why they gave a one-month grace period without requiring reasons for absence.

And that's why, the less randomness affects the rating, the better it is for everyone...

Tell that to Vasya Pupkin. Right now, you're advocating for the interests of consistently strong players. So, whether it's better for everyone is debatable.
And the point of the rating is lost if it's too stable and doesn't depend on randomness. The current rating is the current rating. And no one can take away the glory of victories - they all go into the Hall of Fame