Sorry to keep on the CAS topic, but I'm going to anyway..
Such is the way of the forum, this it always has been, and thus it always will be...

Is the current problem an issue of mechanics, or an issue of balance / scale mis-match?
Both. In some cases the mechanics more or less force a balance issue which cannot be resolved since those mechanics are present in other parts of the game, unless you change the mechanics entirely.
An example is AA damage, which is modeled basically as a missile hit with a certain damage value. The only way to solve the problems here RE: armor penetration and shock damage is to rebalance those mechanics for the entire game, which is excessive. The way AA weapon damage is calculated is also not really balanceable unless we change it entirely - right now, for example, LAA is
useless until Racial Attack tech level 10 or higher, but due to quadratic scaling AA damage (particularly MAA, since HAA is not as widespread) quickly becomes overwhelming beyond this. The ends of the scale are both too extreme by nature of the mechanic design, it is not a simple tweaking-of-numbers problem.
Would tens of fighters be expected to make much difference in multi-million ton land battle in the first place? I feel like in terms of cost per unit, and speed, fighters are out of place in planetary combat in the first place. That makes me feel like the damage and armour are mis-matched as well.
To be honest, this is an argument in favor of a new GU class, which is the easiest way to resolve these mismatches.
The "tens of fighters" issue is actually as much a logistical/strategic problem as a micromanagement problem, as to be frank actually developing the carrier/deployment capacity to bring 100s or 1000s of fighters to a ground invasion is almost prohibitively expensive... notably, unlike troop transports it doesn't really work to build GSF carriers as commercial vessels because the fighters need to be maintained which requires military hangar bays. As building a large dedicated wing of GSF carriers is usually going to be impractical this limits the use of large GSF forces to fleets which already have carriers and can swap the fighter loadouts as needed.
However, at this point... does it really make sense that only a few very rich and arguably over-developed navies can deploy an air force, when in real life air forces are a critical element of every major military force? Why is such an ubiquitous combat arm locked behind so many gates and hurdles? By making air forces into another GU class you resolve this problem as well.
I'm just spitballing here, but what about a re-balance of fighter stats when operating in ground combat, combined with some QOL to help manage assigning them. After all, 1km/s is faster than most fighters today. I'm imagining hangars filled with loads (hundreds?) of fighters that are all tiny compared to space fighters, that are still able to actually survive and have an impact in ground combat due to stats being buffed. Managed with some QOL tools to auto assign squadrons to go and support ground formations, or go on interdictions tasks.
The problem is, how do you do this without creating exceptions to the existing fighter mechanics? Analogously, the major reason that fighters in Aurora are
not tiny (~10-ton) space-based analogues of airplanes - unlike in most sci-fi settings - is because it creates exceptions in the rule where tiny fighters can bear far more firepower (per ton) than large vessels, which doesn't make sense (if, for example, a 2-ton fighter autocannon is as effective as a 300-ton Gauss cannon, what prevents large ships from mounting dozens of the 2-ton weapon instead?).
Under the current rules, I've generally found that you can create fighter pods which are about as efficient as the corresponding ground component (B, AC, or AA types) if they are about the same size as said component (e.g., ~20 tons for light and ~40 tons for medium). This practically limits GSFs to around the 50 to 100-ton range depending how heavily you want them to hit. If you want to push GSFs down to about 10 or 20 tons, you need to have
effective fighter pods which are significantly more size-efficient than the corresponding ground components, which is the same kind of problem I described above. If you instead use an aircraft GU class, it is very straightforward to implement mechanics which are naturally balanced and self-consistent, once the actual mechanics are coded in for air units (which I will acknowledge is a big pile of work for Steve).
I don't know, as I've not really messed around with CAS myself. My feel is that it's a balance and micromanagement problem though, not that the CAS mechanics are broken per-se. (Well, other than AI not using them).
Related to the AI non-usage problem, another big issue is that with the current mechanics, only one side can use an air force and it is the side which has space superiority - in practice, always the attackers as space superiority is required to launch a planetary invasion. This means a defender can pretty much never deploy an air force which is pretty limiting (and makes AA basically pointless for offensive formations, which is silly). If air forces can be modeled by ground formations a lot more space opens up for use of air forces generally, which is at least a big benefit for roleplay.