I can't rank either 2 or CE because too much nostalgia. Although I feel like both would be above this, but Halo 2 only gets such a good spot for BxR, double shot, and quick reloads. Without those glitches I would rank it way lower.
You just named several of the things that made H2 worse than H3.
H2 would easily be the best Halo game if not for the glitches, cheaters, and stupid power weapon system where often the power weapons would not respawn so long as they were being held.
Those things combine to make H2 the best tournament level Halo game, but they make H3 the better online matchmaking game.
Those things separated the elite from the casual cannon fodder. The BxR just balanced the inclusion of the sword, all the other stuff required skill and gave people that were already good a huge edge.
The Chief: "...you are also getting a new partner" Blasto: "Are you engaging in reproductive behavior with this one?"