"Balance the flak so that if this ratio is there, and if strikecraft fly within range of the flak, they are dead. Period." Do you mean "give them a few minutes" die or "kill them on sight" die?
I mean that, conceptually, the strikecraft are "countered." Now, if you say that it might take several minutes to kill the strikecraft with a particular flak balance, meanwhile the strikecraft have destroyed everything in the system before they are dead, then that does not sound like "countered" to me. Thus that particular flak balance isn't any good. If you say the flak killed all the strikecraft, but the strikecraft were able to take a couple units out before they died, that sounds more "countered."
It's like anything else. If you send 50 cobalts into my planet, I should be able to counter you with X numbers of lrfs, and that counter should work before my system is laid to waste. In other words, if I have the proper numbers of lrfs in my system, I WIN. If my system is laid to waste, then I didn't win, I lost, and the balance isn't right, and thus the counter is not viable.
Strike craft are different from other ships, in that they can escape from the fight at any time by going to dock, or the carriers can pull them out by jumping. A fighter who is "deep in the thick of it" is just seconds away from escape. Any real combat frigate may need more than a minute to pull out, while they're not shooting, while they're vulnerable, which is a BIG difference. So when you say "They're dead. Period", that suggests a severe and unescapable demise, something that counters even their unbelievable escape speed.
To simply ask a (hypothetical) question, would "severe and unescapable demise, something that counters even their unbelievable escape speed" be a problem? Off the top of my head, it doesn't sound like it to me. However, I also know that you should never do jack shit off the top of your head, and the devil is always in the details. But humor me - tell me what would be wrong with this, just so we thrash it out and get it on the forum for others to ponder.
However, the nature of its unlimited range, infinite ammo, quick retreat, and hard fought swarms means that the carrier can stand on its own as a main battle ship with little need for support.
I have no problem with unlimited range - that is the point of a carrier (actually, the range isn't unlimited - it's limited to the grav well). I have no problem with a quick retreat - again the point of a carrier. Here you are delving into "tactics territory" as DorianGray does. Also, infinite ammo is nothing because all ships have infinite ammo.
Tactics, range, etc. isn't the problem. Even your "this should be a support ship, not a main line ship" isn't the problem (I'm not so sure I even agree with that contention). If there is a problem, it is simply counterability. Period.
So the first question that needs to be asked is "what is the counter supposed to be?" Intuitively, I look on my ship list and see something called a "flak frigate." Well, if this isn't supposed to be a counter, then what else is it to be used for? Window dressing? A potted plant? Is it sort of like the PJI when the game came out? Something which costs money but does nothing?
Now, if flak is supposed to be a counter, then the question becomes "does it actually do its job?" If the answer is "yes" then we move on. If the answer is "no" then the unit should be adjusted.
Question1: what are the "bona-fide" counters to carriers?
Question2: are those counters effective?