the reason it's unfinished is because MS forced the release date.
The reason it's unfinished is because of the widely known problems in production. Due to poor management, after the (awesome) E3 2003 demo, Bungie had to scrap pretty much all their work up to that point. Their campaign was an incoherent mess. The engine had to be scaled back because of limitations with the Xbox hardware.
Every time Frankie gave the illusion in his weekly updates that things were going well, it was basically panic mode behind the scenes, with Bungie being in crunch mode for a year just to get the game shipped.
That's (one reason) why so many features like Saved Films and online co-op were initially in there, but got cut before release. It's why the multiplayer balance was terrible at launch (requiring a huge rebalancing of grenades/melee damage to make them more potent). That's why there's a massive cliffhanger ending.
Yes, MS did put a lot of pressure on Bungie behind the scenes to get the game finished by Fall 2004, but it's hardly like they did not have the time in the first place. Bungie had 3 years, and threw away 2 of them. Meanwhile MS wanted that killer app that they'd been paying for (and got, despite the problems).
In some ways, the very notion of H2A is insulting to Bungie. They know they fucked up badly with H2, and H2A is parading it around (or the campaign at least) as a massive success. There was no dispute with CE, which had a very highly regarded campaign and multiplayer mode, and is widely credited with making the Xbox viable.
H2 MP's legacy is undeniable. While there are flaws in it and I seem to recall Bungie were unhappy with certain aspects of it (judging by Chris Butcher's comments a few years ago where he stated that he couldn't play the game because it was so far below his standards), it's one of the best multiplayer modes in the series and deserves celebration, for similar reasons to CEA. If 343i take various comments to heart and fix the things that let it down, it will definitely be well-received and could easily revitalise the franchise after the disaster of H4's MP.