Over the last few day at E3, there was a reveal that the game Happy Wars was supposed to be a cross-platform game and a number of gamers are cheering for finally being able to play people on another console. Even though the aspect of cross-gaming is hardly pursued, both developers and the big three console makers are obviously missing the advantages of gaming across platforms.
First, there would be a Huge community for their games, doubling, tripling, or quadrupling a gamer's favorite games; so even the games that don't do well initially will still have a huge gaming community, which could increase the games sales overall for slow to sell sleeper hits (considering a strong online community is a considerable factor for purchasing older games), and if games have a significantly stronger online component rather than a single-player component, even if the game tanks in reviews the developers could have a second chance through the reputation of their online portion of their game; perhaps even making a rally despite having a weak single player campaign, setting themselves up for another chance through a sequel with a hopefully wiser, more fun-focused single-player campaign.
Next, temporary exclusivity will become relevant when first stepping on an online game when the other console has even a 30-day head-start, which would bring up a curious duality: the amount of temporarily-exclusive games will increase, which would increase revenue for developers, which would cost console developers, but could be theoretically beneficial due to the possible offset by gamers buying the earlier version of the game should go up significantly. As far as making DLC temporarily exclusive, well, there's an old hot-dog vendor saying: never make a man wait for onions. What I mean by that is although a person may want to have a little extra bells and whistles on their dog, most people will walk away if you leave them waiting, even if they wanted it. The protest potential for the already unpopular method of paying for downloadable content would likely be high. Obviously this would not work for dlc but it would motivate people to buy DLC as soon as possible so they can get good at the new maps because of the large community of fans playing together: most likely from the console fans who didn't get the game first.
Lastly, a lot of cross-console hostility will cease. There will always be exclusive games, and I think there should be to best express the nuances of each particular console, but when it comes to games that are on both consoles already, this represents an opportunity for game players to come together for what matters: to game. A lot of gamers in the end really don't care about the kind of consoles another person has, and they only serve to cause strife to people who have more things in common than their differences of choice. Communication between game owners in the end could prove beneficial to developers and console developers alike, as actual friends that own different console can get an honest opinion of how a game really is, without the advertising hype or fanboyism associated with most game reviews out there. To have a trusted buddy tell me an honest opinion about an exclusive like Killzone: Shadow Fall, Ryse: Son of Rome, or The Next Zelda game is worth more to me than all of the accolades that IGN, Kotaku, or Gametrailers could muster on a game.