I have a better idea:
The problem with E-sporting Planetside is in the instancing. You can't shoe-horn that into the open-world sandbox.
However, there is an analogy within Planetside already: Core Combat
<groans from the crowd>
Hold on a second before you pass judgement - this is similar, but different.
First, there wouldn't be any caves. This would be something else. More on the arenas in a second.
Second, these would not be "always open" like the caves were. You'd have to "sign up" when it became availible and once you lost you'd be out. More in a second.
The inspiration comes from Global Agenda. Global Agenda (GA), for anyone who doesn't know, is a fully instanced FPS "MMO" with match making. The proposal takes the best from their system and merges it with the best from Planetside 2. Here's how it works:
Along with the continents you have 3 "Special Installations" that are completely separate from the continents. These could be something along the lines of what's seen in Glabal Agenda:
Or something completely different - for example an orbiting space station. The main thing is that they'd be much larger that the Global Agenda arenas and they'd be cut off from the main continents. They'd support up to 600 players - 200 per empire.
Like Global Adenda, they'd be timed to open on a regular basis. There would be a timer and an all-call in the warpgate footholds. Players would have a very limited amount of time to join in the match, and matches wouldn't happen but only a few times a day - maybe 4 times - once every 6 hours.
Players would board a transport, much like a Hart and they would travel to these arenas. All three empires would arrive at once, and once the players were deposited, the transport would debark.
Now it's a fight to the end for domination. Each empires must force the other two off by capturing their "home flags". The last empire standing wins.
What they win is a huge resource boost. Each of the three arenas would boost the one of the three resources and if an orbital platform is added, it could grant increased pod-drop access.
Once the special arena is won, a transport arrives and the players are put back at the warpgates they came from.
The lore is easy to fill in around this system - the facilities have a limited power source that must be replenished since they are not on the global grid. The facilities must be secured before they can be powered. Powering them locks them from being accessed. When the power runs out, they are once again open for attack.
This gives E-Sport enthusists the controlled arena battles they are looking for and ties in nicely with the rest of the game without disrupting it. If you don't want to participate, then you don't have to.