Perhaps to give a similar goal for building up good weapons as Crucible, why not include a sort of survival mode that is similar to Gears of War Horde mode, or Halo's Firefight mode? The goal could, of course, be to survive for as long as you can against different waves of enemies, maybe even including some of the tougher enemies like Walkers, Archon Priests, giant Hive Knights, or Cabal Commanders.
The waves could of course be increasing in difficulty, and every so often a modifier can be thrown in as either a challenge wave, or just in general to increase difficulty. Occasionally new drops could appear for either ammo, increased cooldown, or something like the Sword of Crota or Relic could temporarily be available.
The beauty of this is that the game could be entirely built around one goal: killing Guardians. The AI could be improved, new combinations of enemies can be implemented, multiple spawn points from multiple directions... the possibilities are endless! Not to mention, currently the only real "purpose" of weapons in the end would be to take the into Crucible, or go into Raids, and since Raids have no matchmaking, it's not like you can go in and show off your awesome PvE Weapon you spent hours grinding on.
This could also offer rewards in a similar style than Crucible (or perhaps better). I think this is much more engaging than just going into Patrol and finding a small squad of enemies that are super low level, or going into a mission I've replayed a dozen times over.
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Wouldn't that be awesome! Is Bungie going to implement it? Of course not! :D My hopes and dreams are all dead :(
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I can't stand this type of thing for long before getting burned out, but hey, I don't see why not because it'd prob only take em a weekend to do. They've got the monsters and the maps already.