So to the poster's question, " How do you keep a PvE player in the open game when they could play in greater safety in solo/private?"
Surely the answer is to make it challenging, interesting, and above all, a worthwhile experience. The differentiator for Open is other players so the challenge, the interest, and the worth needs to involve players.
People don't play games for safety, now do PvE preferring players see other players as a "challenge". They are just people they encounter. Some are friendly, and maybe worth a line or two, or a quick voice chat. Some you cooperate with, maybe help them out when there's a pirate attack. Some are comrades in arms for bounty hunting or joining a warzone.
Playing with other players can be a lot of fun, and enhance the game for PvE focused gamers. The fun isn't in melting their faces with a beam laser though, and they aren't there "to make things more challenging", except maybe when they are racing you for the same mission or time-limited trade opportunity.
What can spoil it is if PvP combat, especially attacks motivated by nothing else than a ganker seeing a hollow symbol on his or her scanner, gets out of hand. That adds absolutely nothing for the PvE focus player, and is just a slap in the face of anybody seeking immersion. "There was no point in that attack, I wasn't carrying any cargo, I had no bounty..."
It's the
senseless part of senseless violence that I and many others object to. There are plenty of reason to let the guns do the talking in Elite, but just seeing another human player isn't one of them.