I think destiny should work on bringing both elements together.
Example: World of Warcraft's Alterac Valley BG
In this example they have elements of pvp but on the side, it had pve elements to accomplish if your not that great at pvp. The things to take away from Alterac Valley is: Map size, player size, tug of war elements, pvp/pve elements, side quests, npc support, and a boss fight on each end.
With those elements in place, destiny could make a big zone map, much larger team sizes, and objectives to defeat the other teams boss/leader.
Another example: smite/dota/HoTS
Smaller player teams, but includes npc support and the map size is not as big as Alterac valley but still big enough to give everyone an advantage.
I know it's hard to make with the destiny elements of being a shooter game. But I think this would be a fun element to play with.
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No! They tried something like this with The Division and it turned out to create super powerful troll teams that spend their waking life playing the game just to terrorize and kill everyone for the hell of it. Unless you aspire to be a troll that does nothing but grief players then this is a bad idea.