Halo 3 sold what it did for two reasons:
1) it was set up to by Halo1/2 success ensuring there simply where many, many millions of people waiting to buy the game.
2) it was a good game, that delivered pretty much what the existing fanbase wanted.
Put simply it couldn't fail (unless Bungie literary raped the gameplay) and other titles would have made little difference, whether there where few or many.
Look at it this way - when the third LOTR movie came out pretty much everyone with an ounce of sense knew it would pass 1$ Billion at the box office. It didn't matter how many other films were around nor how good they were. It's audience was ready, preped and unless the thing failed to deliver its success was guaranteed.
So no, sorry, it's got nothing to do with lack of exclusives, little competition or whatever. That might help explain Halo 1 but not Halo 3.