I've always played it for the story. Just recently I've begun to appreciate the original trilogy's (books and games) story. The best example I can give is when I first played Halo 2 I hated the Arbiters missions. I hated them so damn much and thought they where drawn out and boring.
Being quite a bit older now and playing through the originals again I can really see the story couldn't have ended where it did without them. Do I still think Chief should have had some more missions? Yes, but what can you do.
I don't know hat it is but I dont find the H4+ series to be as interesting, but maybe I have to read the new books to appreciate it and get the full picture.