Not sure if this has been posted before, and I don't mean to suggest that I have any problem with the way Patrol is now (that's my meat and potatoes), but I was thinking the mode would be a lot more engaging if there were "hidden" stories offered occasionally by the beacons.
I'm just imagining a setup where, less often than the "go kill this target" bounties, Guardians would get a bounty that would take them through a few steps, to an eventual mini-boss and a (greater) possibility of a Legendary drop or materials. They'd basically play out like normal stories, so when a Guardian enters a spawning-restricted area, they move to a separate instance of the map for the purposes of completing the bounty. Afterward, or after dropping the objective, they'd be moved back to the main map instance with everyone else. These bounties would have more, clearer lore tidbits than normal ones and would reward 50 - 100 rep, depending on the challenge of the particular bounty. This would serve as another--possibly more compelling--incentive to Patrol.
Then again, there's probably a lot of folks that hate Patrol and would QQ because they'd view it as "inaccessible content" or something.
EDIT: Fun to note that the Destiny Grammar Police, like the everyday kind, sure are apt at administering correction despite a preponderance of evidence.
EDIT 2: Also fun to watch "likes" for this post fluctuate as people decide whether their abhorrence of poor grammar outweighs their support for a solid developmental idea (not tooting my own horn, a lot of folks seem to like the direction of my suggestion).
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..so basically you suggest, change patrol mission in 'not strike bounties' which already exist. don't get me wrong! I do like concept of your idea! but this game extremely lack in content and such change would make those 'not strike' assassin bounties even more meaningless and useless.