No, a PvP player must work a lot harder to maintain their credits and ships than a PvE player. They lose money every time they PvP, whether ammo, ship damage, bounties and fines, etc....so they not only have to play to PvP they also have to PvE to be 'allowed' to PvP.
You are thinking the ONLY reason someone should do something in for intrinsic reward. My point is that providing danger to the game can be considered a service...seriously. There should be some extrinsic reward given for that. Unfortunately, the game design precludes this from occurring...since no one can provide the same service from Private modes. So, there is no extrinsic reward, and players have to decide to provide danger, at a strong cost to themselves and their preferred play style...or play for the extrinsic rewards given.
There are only two types of players that would do this, and pay for the privilege....those in it for intrinsic reward...the Role Players...or the blackguards who want to see people suffer and stew..again intrinsic motivated people, being naughty because they can. At that point PvP should cease to exist within the Open galaxy. Not because the people won't play those parts....but because their numbers would be so small, and diluted, that they would matter even less than they do in Open now.