I don't really see the appeal of PVE in open. The reason why you'd be in open is to play with other players, and right now, the only viable gameplay involving other players is shooting at each other.
The Explore/Trade options are basically solo experiences, unless you want to go far out of your way to make it a group experience and then you're spending most of your time waiting for the other guy to show up, just so you can jump again. There are wing missions, but those are basically solo missions that the wing gets rewarded for and not a great example of group play.
AX Combat can be done in a group, but because space is really big, the likelihood of meeting another AX pilot drifting around space looking for a bug hunt is pretty low.I believe Drake has an equation that could be used to model this probability.
Basic pirate killin and bounty hunting does exist, and can be a rewarding. People often complete these sort of missions in wings. Though, the completion is a sort of modified version of the mission. Wing pirate extermination missions usually involve a wing of players visiting a threatening signal source and fighting off a well equipped wing of coordinated opponents. The more common approach to completing these missions is to park a T10 in a RES and go do something else for a few hours. Then, after the wing missions are complete, the wing shares the rewards of their individual efforts. Arguably, not in the spirit of the mission.
So, even if there was a PVE mode in Open, I don't think it would be any different than PVE in solo. You'd still be doing exactly the same stuff. You'd still be floating in space all by your lonesome, never seeing another pilot, only getting interdicted every few hours while the Navy searches your hold for contraband.
If Open were to be made viable or interesting to PVE players, there would need to be improvements in group play, actually fostering and encouraging players to cooperate in real time and in real space together. Simply adding a "No PVP" flag would not get me into Open.