Several different people have been hitting me with that disagree, so I'd like some more information if you're willing to give it. Could you please just tell me more about what you're doing with all the aircraft and what your role as the air controller is?
Basically, the air controller just manages the entire faction's combined air force. This saves on research as only one member of each faction needs to research an air doctrine. Every major still researches and produces planes, but they all lend-lease 100% of their production to the air controller, and the air controller also receives as much fuel as needed through lend-lease as well. Typically the air controllers for Axis and Allies are Hungary or Romania, and Canada. This is due to those countries having either the best focus tree for rushing fighter 2/3, having high command that gives +3% air superiority atk/def/agility(Canada has 2), or both. Romania has a better light air designer at +15% agility instead of +10%, whereas Hungary can rush fighter III with an ahead-of-time reduction, so there are valid reasons for both to be air controller, and both have been meta at some point or another. I haven't played MP in a while, so I don't know who currently does it.
Also, Germany's "Jagernotprogramm" decision enabled them to cut fighter production cost by 25% by increasing production cost of other aircraft by 25%, lasting 180 days. in earlier versions of the game (i want to say until 1.7 or 1.8 but I can't find it in the patch notes), this decision was repeatable as long as you had below 750 deployed fighters and 350 in stockpile. I'm sure you can see how this was exploited with the use of an air controller. By lend-leasing 100% of its aircraft production to the air controller, Germany was basically able to just permanently have 25% cheaper fighter production due to never having an air force bigger than 1100 planes. This exploit was fixed in a patch as the decision can now only be taken once which makes it not nearly as good(though the decision is typically banned anyway). The intended use of the decision was for a Germany that is horribly losing the air war to be able to crank out fighters incredibly quickly. The intended use is now almost the only possible use, but once you've lost the air war you're not coming back so it might as well not exist.
Another reason for having an air controller is that when multiple allies are flying missions in the same air zone, fighters will not escort allied (not same country) CAS or bombers. This isn't that big of a deal, but it should be noted anyway.
Air management is the same as in a normal game, just a different player has control over it. One player gets to devote all of their mental focus and time to making sure planes are always in the right air zones, keeping green air over theaters of combat, defending against strategic bombing, bombing naval routes, etc. The added focus can be important for taking down planes if not trading favorably to save for when you need your numbers at a key point in time, and things like that. A player on Germany will be having to manage so many different things like microing tanks, managing focuses/research/spies/everything else, and might not notice that they're losing fighters 2-to-1 and lose most of their air force.
Air superiority gives enemies a really hefty penalty to defense and movement speed, and in multiplayer nearly all gains are made via encirclement. Encirclement can become hard or impossible under red air against a good opponent who knows how to micro defensively. AA can reduce the penalty but can't remove it completely. The main value of AA is in shredding CAS which it does very effectively, but if you lack air superiority you're still going to be slower than the enemy and have a penalty to defense from the sheer presence of enemy planes. USSR is usually going to have slower tanks than Germany anyway because it builds heavies vs German mediums (unless Germany goes heavies now too, I'm probably a year behind the meta in terms of playing "competitive" games), so it doesn't really care about the penalty. A USSR who does do air can be key to an Allied victory however, because this forces the Axis to choose between splitting their air force in half during D-Day situations, allowing the USSR to have uncontested air over the Eastern Front, or allowing the Allies to have uncontested air over France.
TL;DR The philosophy that I've always seen in MP and agree with is that air superiority is key to winning the war in MP as the Axis or Allies, and air controllers are the most efficient way to manage air in multiplayer.