So, because their race is more important, they should have less say in how it's run? I'm not sure I like that direction.
In sportscar racing, the Le Mans 24hr Race is the one race which is seen across the globe. It is the absolute pinnacle, the face of international sportscar racing.
Because the FIA recognise this, they homologate their GT series based on ACO (the runners of the 24hr) rules so that their GT teams can participate. The ALMS and the LMS, two of the most prestigious sportscar championships in the world, include Le Mans in their name, and run to an approximation of ACO rules. The ACO gives out automatic invites to the winning team and runners-up in these series, but overall, the people at the ACO are given absolute control over how they want their race to be run and who they want to be there. You may quibble with their selections but, ultimately, they should be in control since it's their race that the world sportscar calendar revolves around.
Similarly, the ASO have the biggest race on the calendar. The fact that they have the biggest race on the calendar by far in the eyes of most people (mostly casual, non-cycling fans) acts as vindication of their policies to date, and that their race has not diminished in lustre is an indication of their competence to run it, therefore the control over it should not be taken out of their hands.