Rare will never introduce PvE modes as it would undermine the core concept of the game, and I applaud them for it.
That said, as someone who's sticking with it, I still maintain its the best Pirate game I have played in my entire life, and its only getting better. I'm particularly thrilled with the new damage system they introduced with the anniversary update, now actually being able to damage key parts of a ship such as the helm, capstan and all of the masts. Artillery battles now have much more tactical depth to them rather than just focusing on poking holes on other ships.
I swear, I've had moments that have almost felt like in the opening scene of Master & Commander where the opening volley just wrecks havoc with everything aboard ship, and the game now even has real fog to boot!
The Arena is... interesting, not quite my cup of tea since I prefer the random and emergent gameplay of the primary game mode(adventure more), but its definitely something nice to just sit down with if you have like a half hour to kill, as each match only lasts 20 minutes.
It's not a game suited for everyone, and it really doesn't have to be. But its one hell of a ride for those that have the stomach for it. And even then its still an extremely forgiving game unlike some of the MMORPG's out there that make you grind your butt off for a ship, and then penalize you severely when you lose a battle.