I think that there should be something similar to forge mode in the upcoming Destiny Sequel, because of how it felt as if you were playing something new every time you got on Halo. It's one of the key things that kept Halo so unpredictable and fun because it wasn't non-stop campaign and multiplayer. Actually, me and my friends had more fun playing forge on Halo than the other game modes. We'd group 8 of us together and we'd start going through all the maps and game modes created by the community, and we'd be laughing for hours. Those were some of the most fun times I've had playing a video game. This would join the community together and give us a chance to see what other players would build.
If you don't think that they could make sense out of it since the game is a co-op MMO. Well, they could in the same way that competitive multiplayer will, you'll have to go to a specified in game location. The location can be justified with whatever suits the lore, traveler holographic training room, ancient lost civilization technology, whatever. If you think there should please add on to what I think.
And if you think there shouldn't, give a decent explanation of why you think that forge mode shouldn't be in Destiny.
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We don't have the customisation options we did in halo, specifically weapons (which aren't scattered around the map), vehicles (they generally don't fit the smaller style of map) and the multitude of other random objects halo had in it (teleporters, explosive barrels by the bucketload etc).