I think it is simply because Modern Warfare tried to push the War genre pass what it had been on consoles since Medal of Honor: Frontline. Up until then most games were essentially clones of that game. Modern Warfare really changed that by not only changing the setting and time but really turning it into something more than just a war shooter with a sub par storyline. Even further, it made large advances in the online territory for the genre by actually giving it a fair amount of death.
So really I don't think it has to do with timing or generation differences but simply CoD took the war brand with Call of Duty 2 on 360 and PC and then changed it forever with Modern Warfare to make it a more cinematic experience with great multi player.
I don't adore Modern Warfare in anyway (I do like it) but I do think it was an influential game release this generation.
Essay Pro