Personally I agree; I'd like it to be like that, and I'd enjoy playing in the PvE galaxy without needing a workaround like Mobius. But what you're overlooking is that not everyone wins.
1. PvEers are already playing the game they want to play. In your proposal they would continue to do so.
2. PvPers wouldn't be playing the game they want to play! Other games have gone this route (and I don't rule out the possibility that Elite might yet do it); what always happens is that the PvE server becomes the "real", populated game, and the PvP server becomes largely deserted. Reading this immense thread carefully, you can often see this fear expressed when a PvE mode or a PvP flag are suggested.
The 'flag' proposal isn't analogous to what I've proposed here.
Flags just remove the [Mode], putting everyone together in [Open]. Both groups of players would still be working in the same BGS.
PvP'ers make the same argument against flags that they make against the status quo because PvE;ers would still be invulnerable to the PvP'er, while undermining their faction/power.
Split Galaxy/BGS fixes this. Everyone choosing to play the PvP Galaxy would be by definition a consensual target. No grief, no salt.
It would mean the PvE'ers can do away with PG member limits, no risk of infiltration and maximise the chances of encountering other PvE'ers out in the void.
Win/Win/Win
Plus One this post and bounce it into the Suggestions box.