I've had a couple of thoughts, they don't necessarily synergize all together, but maybe a few in combination might improve Aircraft gameplay.
1. Increase air vs air damage.
2. Reduce all damage air vs ground, but give Logisitics as an auto-promotion (or adding a 3rd strike possibility, i.e. Logistics 2 or something.) The damage reduction would account for the more attack chances, but the more attack chances per turn would keep planes relevant by allowing for several attacks per turn.
3. Buff/Nerf planes even more than they are as it relates to their specific intended role, i.e. Interceptors(only really effective vs other aircraft), Ground Attack(only really effective vs ground units and less so vs other aircraft and cities), Bombers(only really effective vs cities or tile improvements, maybe somehow reducing the defensive bonuses provided by the improvement? Bombing a fort or bunker may not severely damage the units within, but they significantly receive less defense vs future ground attacks as a result). Pretty much setting Aircraft base stay bonuses even more so to restrictively encourage their uses. The Ju-88 specifically seems OP to me as I can do significant damage to ground units AND go bomb cities AND ships, especially as they gain promotions.
4. Restrict coexisting promotions? (Disallow obtaining +attack vs armor and +attack vs cities, etc.)
5. Instead of 4. maybe modify the bonus that promotions give to effectively restrict the diversity of role? For example, taking a promotion might give [+% vs Cities] AND [-% vs Ground Units] or something along those lines. I know in real life aircraft are able to take a variety of ordinances depending on the mission, but in Civ it might be worthwhile for balance to restrictively limit the roles of the aircraft.
6. Potentially reduce ground attack damage vs units in cover? As difficult as it should be for a Ground Attack plane to hit individual infantry in open ground, it should be far more difficult to damage them in a forest. Bunker busters might be a good addition as a specific role to provide some help vs lines of fortifications.
Personally I would like to see more specific roles for aircraft (whether that is determined by their base stats or their individual promotions chosen), less damage overall vs ground, and really MORE Logistics Promotions. Time is funky to think about in Civ as a turn based game and makes many balancing aspects challenging, but I feel like planes should be able to run more sorties balanced by their greatly reduced/balanced damage output.