Halo 2 is far and away my favorite game in the series, but that's because the single player of each one has very little impact on my enjoyment of each one. Halo 2 had far and away my favorite maps and gameplay as far as multiplayer is concerned. I played so many thousands of Halo 2 matches that it's ridiculous. I played plenty of Halo 3, Reach, and 4, but none of those come even close, in my opinion, to the masterpiece that is Halo 2 multiplayer. I always felt that equipment in Halo 3 was broken, and so never enjoyed it as much as I perhaps could have.
So while your points about the single player are absolutely true I just can't hold anything against Halo 2.