I have a "big picture" theory...
PvP in Elite is unpopular for a number of reasons...
1) Space is big. Really big... and it's also very, very empty.
A lot of the time, if you're fighting one spaceship with your spaceship, it's going to be out in space, away from asteroid belts in empty space. There is no cover, nothing to hide behind. This means that the battle is always going to be jousting or orbiting within that 3D volume and with 6 degrees of freedom of movement.
Every time, it's a battle of attrition - who will wear the other down first? Whose shields will fail first? Whose modules will wear down quicker? Whose hull will break earlier?
Ultimately, if you've been through one Space Fight, you've been through them all - and frankly, this is boring. If you've watched one recorded video of a fight in Elite, you've seen them all. They're really, really boring to watch.
The only exception to this is fighting in an asteroid belt, where you have places to duck behind, and it is a bit more interesting to take part in and even watch on video. But those fights happen less than the majority, which are in open space.
2) Lack of any meaningful Crime & Consequence system, and/or Karma system...
Currently, and since release in December 2014, the consequences for being blown up far outweigh the consequences for the player who perpetrated the blowing up of another player's ship. The game does not care about why a ship was blown up. The punishment is almost always entirely dealt on the player whose ship was blown up - maybe it's an explorer who's been out of the bubble for months and has just lost multiple tens of millions of credits worth of data, plus a ship rebuy? Maybe it's a trader who's just lost all their cargo plus a rebuy?
Meanwhile, the player who blew up their ships gets a tiny fine in comparison - and that's if the blowing up was done in non-Anarchy space.
Basically, this game actively rewards those players who choose to indiscriminately kill every other player. It's not financial rewards, though, it's the rush of dopamine the miscreant players receive. Which this game gives out in spades.
3) Lack of good reasons for fighting.
At the moment, the game gives you some pretty weak reasons or motivation for fighting...
A) To prove your mettle/skill?
This seems like a good reason - but at the end of the day, point (1) above reigns supreme. It's more like a battle of attrition than of skill - maybe the skill is in how you've outfitted your ship? In that case you're going to be grinding for the most damaging weaponry and perhaps the most shields or armour on your ship? Ultimately though, you're both jousting/orbiting each other in empty space.
B) You're fighting your Powerplay enemy?
Not that much of the player base cares for Powerplay, a lot seem to partake in it only as a means to obtain whatever toy the Power rewards one with, after 4 weeks of participating in it.
C) Piracy?
Due to point (2) above, piracy was still-born. No Crime & Consequence system means no pirate can be deterred from blowing up another ship. So traders, explorers, miners etc. simply cannot trust that the player who interdicts them, is genuinely playing the pirate role. Piracy is dead.
D) Bounty-Hunting?
Same fate as Piracy due to point (2) above. You can't be a bounty-hunter and live off the proceeds purely by going after other miscreant players.
E) Ganking
Being ganked is tedious, and boring. It is never something to be feared as such. To the player being blown up for apparently no good reason other than 'just because', is just dull. You've been ripped out of supercruise by one or more gankers, and they've quickly destroyed your ship - it is not exciting game play, it's just tedious, especially if you've had this happen a few times.
The game rewards the gankers though, as outlined above.
In summary - space fights are boring as hell, and there's no particularly good reason to be involved in them.
Here endeth my 'big picture' theory.