And CP 0 did not participate.
Other World Government members that were not involved:
Kong's role is simply bigger than Navy HQ. It doesn't show that he lacks plot importance, more that his importance to the Navy is limited and that makes sense given that he is not a member of the Navy.
And yet Navy HQ and Mary Geoise are located in completely different places.
A second Marineford to defeat Navy HQ leaves Mary Geoise untouched.
I don't think there will be 2 final wars just separate battles at Navy HQ and Mary Geoise.