PLANETSIDE 3: avoid the problems of PS2

The biggest problems this game has can't really be removed or fixed (maxes, 3 factions, a unique and fun but goofy flight system, cloak, HA shields, insane anti-infantry vehicle weapons, render limitations for fast moving vehicles...) Basically everything they didn't put in PS:A,

But all of those have ways to fix them!

MAX's: They fall into the extreme cases where to make up for their advantages they need too big disadvantages. By lowering the difference between it's healthpool versus it's speed and counters you can balance them out more.

3 Factions. What's the exact problem here exactly? I think you are aiming at double-teaming. That can be solved through better goals and rewards for achieving them. Currently it's the gameplay that encourages players to focus on the weaker faction if you want to win at the alerts for example, not the simple fact that we have 3 factions.

A unique and goofy flight system. Yeah I removed the "fun" part as it's anything but currently. Fixing it is easy: Change the inverted skillcurve to the skillcurve we have for everything else in the game. This can be done by introducing more intuitive controlschemes as alternative options, adding more inertia and physics to the aircraft (which considering how they behave when unpiloted shouldn't be an issue), allow the aircraft maneuvers that are less predictable by the opponents so that normal flight maneuvers become viable.

cloak. What's the exact problem? OHK mechanics that prevent enemies from proper reaction? You can introduce more mechanics and gadgets to detect them beforehand or remove or change the OHK mechanics in favor of debilitating hits (a headshot causes a concussion effect making it easier to finish but allows the opponent to react) or by forcing the weapon to reveal to the target that a sniper is aiming for them prior to firing (but not necessarily from where).

HA shields. This is a problem with the HA class being too universally useful for all tasks and the other classes not having enough tasks for general combat. You can make the other classes more useful by adding more goals to achieve that the other classes would be better at. The example I always give is the Forwards Station (now the Router) which was supposed to go to the Medic. It would make Medics important for setting up alternative attack routes and keeping attacks going, but give the LA and Infil a greater role at hunting these Forwards Station's down as they have better tools to do that than the HA. It's a great example how the HA and his shield become less useful while 3 classes instantly get a much more important in the general flow of combat around a base as it's less about direct combat and more about the stragetics and completion of specific goals (placement or destruction of the specific spawnpoint).

Insane anti-infantry vehicle weapons. Give the infantry a large range of resource-costing AV tools to give alternatives to C4. Resources destroying resources is the perfect solution.