Split screen is a thing of the past for many games.
This game won't allow it for numerous reasons, too many to count as to why Destiny shouldn't have it and won't have it.
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It will allow it, as Bungie said they'd be willing to do it. Whether they will do it is different. Also if you just drop crucible, latency/lag isn't that big of a problem and nobody is forcing you to play with other players unless you are doing a strike or raid. In a raid you should know who you are playing with, and in a strike, if you are using matchmaking you don't have much choice as to who you are with anyways.