Tricky one.
Would I like to see a dedicated Open PvE mode? Yes
Should there be a dedicated Open PvE mode? No
In other words, as much as i would like to see it and have a mode where no-PvP is enforced rather than relying on Mobius approving etc, I don't think it would be good for the game in general.
What I would like to see instead, is a proper, working, exploit free, crime and punishment system, one that makes criminals actually wanted, cannot be easily got rid of (no more jumping in sidewinders to get rid of wanted states). Also, to relax a little the penalties for the less severe crimes.
At the same time, choosing a criminal life should have its own rewards - for careers like piracy and smuggling anyway. Something that is lacking (no, i'm not talking about insane profits like LRS provides, i mean playstyle rewards, not just monetary). For those who do murder against unwanted targets, i'd like to the game react appropriately. Their setting foot inside any civilized system should set off alarms everywhere with the system security, and at best they can spend a few mins in system before NPCs are dispatched to hunt them down. In high sec systems they shouldn't be able to last 5 mins without getting pounded. This would push the murderers to live on the outskits of civilization, forces to prey upon those foolish enough to enter uncivilized systems.
How FD could do this, i'm not sure. I dare say they have had many long discussions at FD about how the whole system could be changed, and i guess each session leaves them with more questions than answers.
Anyway, my feelings.