No! Definitely not! (For reasons I put in the comments)
I don't care (I have read the post).
I don't know.
Ok, so I'm putting this edit at the top of the post because I doubt many people have the attention span to read this entirely: if you voted no, what would make you vote yes for split screen?
I have been very surprised that few people have suggested a split screen mode for Destiny. Destiny, I will say, is a fun game without split screen, but it could be better if it had split screen mode. I'm not quite sure, but I would assume that most Destiny players only have one game system of a certain brand in their home that plays Destiny, so if they have a friend over they'll have to find another fps to play besides Destiny. I have heard that Destiny was originally supposed to have a split screen mode, but they decided to take it off. I don't know if that is true, but I know I would like a split screen mode.
If Bungie does decide to develop a split screen mode, make sure it's for co-op, PvP, and PVE. Also, add a mode in which you are able to create a game. This means the host decide the rules, such as which map, score limit, gun types available, how often heavy and special ammo spawns, what mode the game is (clash, control, skirmish, etc.), how many players are allowed, etc.
They could at least add a special offline mode of PvP for split screen for some people who think it would be laggy.
Majority of people seem to want split screen!
Also, as someone mentioned, we need private matches (pick the game mode, map, weapons used, etc.).