My opinion on the matter may be a little biased because I don't like to PvP and never will, but...
PvP in this game is essentially a minigame, much like it was in FFXI. The game itself is the storyline and the things you do in your Eorzean travels. Your trials with the primals or Midgardsormr, as well as your struggles against the Empire. Final Fantasy games have always been story first, minigames galore as a distraction/something extra to do. PvP should not (As it is currently) be a primary part of the game. The struggle in Carteneu is all well and good, but
it's been proven to be a diversion by unscrupulous members of the Uldahnian elite to distract adventurers and leaders alike in a bid to simply make more money
, which makes it a really great minigame, but not a central part of the story. In my opinion this is how it should be.
TL;DR : Want more PvP? Should probably play a game with PvP as a central theme.