So I had an idea pop into my head at why I didn't like patrol mode as an exploration mode. I related it to a couple other games and came up with a couple answers.
1. Not enough variability.
2. Too linear.
3. Not enough reward to explore.
1. The areas are always the same. The enemies spawn at the EXACT same spot. That really kills the feeling of exploration.
2. I get it. The areas of each planet are huge and you need loading times in between each large area, but you have to go down a narrow passage way to get anywhere. You always spawn at the same spot every time you go patrolling.
3. The only thing you find are some glimmer, lame weapons, and ghosts. Ghosts are cool, the glimmer amount in negligible, and the weapons essentially useless.
I suggest to fix this: Dead Zones; unlockable at some higher level. Now, I don't know what these actually do in the Destiny lore, so the names can be changed but here is my idea. Each planet gets a SEPARATE area that is selectable via the planet menu. This place is a LARGE free roaming area where there is no control over what happens. Higher end patrol missions, enemy faction wars, and greater rewards happen here. Think Red Dead Redemption exploration or the Frontier from Assassin's Creed 3.
Oh! And I forgot to mention: there should be more verticality in these places as well. It always disappoints me when I try to get on top on a building that I KNOW I can get on top of, but get pushed back because of an invisible wall.
You gave each class awesome movement abilities; let us use them! :p