Player rating for tournaments across all installments of Heroes.

I think you are sacrificing the global perspective of Tournaments for the sake of each individual one. Rating is global. Even if the leader gets fewer points in a specific Tournament than another player, they will still be significantly ahead in the overall rating. If we remove the bonus for new players, the leaders will quickly pull ahead so much that it will make no sense for anyone else to play. If we are interested in a specific Tournament, then there are simply indicators of the placement. The rating for a single Tournament is meaningless. The player's strength in a Tournament is still determined by their result. But on a global scale, introducing a rating means that leaders need to constantly win to maintain their top positions. This stimulates their activity. For newcomers, there is an incentive in the form of a bonus that allows them to gradually reduce the gap with the leaders.
If the rating does not take into account past performances, we will not see the overall picture. A single Tournament season will be broken down into a bunch of separate games that are not connected to each other. In this case, the rating will be useless to anyone. It is enough to simply look at the tables for each Tournament, and we will see who played and how. But the rating connects the Tournaments into one.
Even with the bonus, all stages of the World Cup are equal. It is simply necessary to take into account the strength of the Tournament. If its coefficient is 0.5, this means that the strongest players did not play in it, and they did not show their best result. What is the point in giving them the same rating as those who fought for every step on the map? But the basic rating of 125 points is the same for all stages.