Honestly I think the best solution is one that's going to come from F-Dev; and it's going to come in the form of more content.
I've been thinking about this for a while now, and I think the trouble here is not that some people want to use PVP mode to behave like, um, mule apertures. It's that they want to do that in an environment where there isn't really anything much to do other than what little players and FDev actually create by hand. And players invent stories that consist of, "This vaguely plausible-sounding reason to blow people up"; while F-Dev are coming up with a developing storyline that's essentially, "These are in-world justifications we think probably explain why these players have decided to blow people up".
Not sure how much sense that made.
See, though, at the moment, what are the options in game? We can fight. If we choose that path it's likely that we're the sort of people who'd enjoy the (supposedly) greater challenge of fighting against players rather than AI - so will probably get on swimmingly in PVP mode where all the pirates/gankers/griefers* are. We can trade. Trading involves loading up your ship and driving from one station to another. Depending what mode you've picked and where in the galaxy you are, your journey might involve contact with other human players or not. But in the end, that's what it's about: go from A to B with cargo. You'll probably spend most of your time in inhabited space, if not busy space with a high player population.
Or you can explore. Some enjoy this - though I'd submit that they're a very particular type of player, and a bit of a rarity. Some do it for the money; some do it to get their names on stuff; some do it just because it's there to do. I honestly thought I'd be an explorer, since in most MMOs - in most games, for that matter - I love nothing more than ignoring the content and storyline and just wandering off looking at the scenery. I took so many screenshots in Skyrim while Stormcloaks and Imperials made life miserable for the civilian population and dragons did horrible things to everyone. Fork That Noise, I thought: there's a gorgeous mountain pass over there that I've not seen yet.
So I fully expected I'd want to do exploration here, but exploring in ED just doesn't interest me that much. Sure, I could be the first person to get up close to such-a-nebula; or I might get to see a black hole (read: patch of space with lensing effect and dots). Or I could fly by a planet and, if I really squint, I can see that the land's in a slightly different shape from the last planet I flew by. Yay procedural generation.
But in the end: what is there for me to do?
And the answer is 'not a great deal'. And I'm sorry to say it, I really am - because I love this game, honestly. I know this post mostly reads as terribly critical of ED, but I actually do really like the game. It's visually beautiful; I love the sound effects, and the feel of the flight model is great (although I'd have preferred something more simulation than arcade, but it is what it is).
It strikes me, though, that the problem this thread (along with so many others) is dealing with is a consequence of the fact that everyone is, basically, still crammed together, even in such a giant galaxy, because there's literally no reason to go anywhere outside the inhabited bubble if you're anything less than the hardest of hardest-core explorer types. Everybody's stuck together in the same relatively small areas of space - the Old Worlds, Sol and Achenar, and the newbie starter area around Eranin etc - because there's just no reason to go anywhere else. Everything beyond those areas is almost entirely uniform - and yes, I know that's a fundamental quality of the universe, but there should still be localised variation.
No-one's got anything much to do apart from Whatever It Is They Do. Explorers gonna explore; fighters gonna fight; traders gonna trade. And with the exception of the first group, who generally aren't to be found complaining about PVP anyway because they're ticking boxes sixteen thousand light years away, we're all bundled together because there's no reason to go anywhere else.
If exploring meant you could fly down to a planet that was procedurally generated in detail, and see landscapes, oceans, plant and animal life, weather that you might not see anywhere else - if it meant actually getting down to the surface and seeing new things, not just watching a scanner go 'ping' to say it's done - then I'm sure I and many others would swarm off to go exploring. I'd love to stand on top of some alien mountain, or a far-distant forest, and take a photo of the moons rising. That would make me feel like an explorer. Yes, I know this is all slated to come SOON, but it's not here yet, and that's my point.
Or if trading meant not just picking up stuff here and selling it there, but actually being able to watch commodity prices, play the markets, place buy and sell orders, undercut the competition, seek out obscure suppliers or discreet buyers - as is possible in A Certain Other Space MMO - then it might well drive people out of their bubbles and into deeper territory. Especially if there are more opportunities for shady-tradey: what about all the lost colonies that must be out there in the peripheries of human-inhabited space? The unregistered settlements on Earth-like worlds; the mining colonies stuck into the side of asteroids; the wandering generation ships? What opportunities for commerce must exist in those little niches?
IN SHORT (too late), if there was reason for people to leave the bubbles in numbers - not just the tiny few who enjoy hopping between far-distant uninhabited systems - then I'm certain that grief, ganking, piracy, player gangs, blockades, ramming, all these things would simply fade out of the limelight as people found other things to distract them.
(* Strike out whichever you most fiercely object to.)