You're right, my ideas weren't really fleshed out and a bit scattered. So for the mid-air refuel idea it's not really a great one but I meant that as a mechanism to enable longer rebase range. My main disappointment which I didn't directly state before is carrier is useless without aircraft. So lets say the only thing to change was that carrier comes with a fighter or has a way to build a fighter without an aerodrome and i'd be happy. Obviously a different genre but in rise of nations you get 7 fighters when you build an aircraft carrier, that's a great return on investment. Then if they die, you can rebuild them. But also in rise of nations the normal aircraft can't land on the carrier, which actually makes sense as land aircraft are different specifications from Navy ones. So for me personally I much rather have carriers come equipped with planes, and let them rebuild them in friendly territory or something.
A bit of a tangent, but in Advance Wars: Dual Strike, Carriers had a similar problem; they sported the longest ranged anti-air atack in the game, but were very expensive, and absolutely pointless in matches without air units. In Advance Wars: Days of Ruin, Carriers lost their long range anti-air, but could build Sea Planes when they had capacity. Carriers were still expensive, and building SPs on top of that was absurdly expensive, so trying to go all in with Carriers + SPs was a bit of a joke. However, it meant that at minimum, Carriers didn't have a strict dependency on requiring the map to have airports to be useful. SPs may have been expensive, but they had the unique ability to hit any unit in the game, and they actually hit quite hard too!
Back on topic, in Civ 6, I wouldn't mind if Carriers could start with an air unit or two of their own whenever they were built, and these could be special air units that were only available via Carriers, or they could be Air Fighters (though that gets complicated with the Alum maintenance cost). I would normally be okay with Carriers being able to produce air units, but building planes on Carriers is highly ahistorical from my understanding.
To be honest, I do like how the deployment works in civ 6 where you can deploy fighters to a tile, that's a step up from civ 5. But I also think it's kind of weird that planes just don't sit on tiles like helicopters do. It's not like supplies and fueling is a thing in this game so why are bombers and jets even tethered to an airport/airstrip in the first place? But this topic is more about aircraft carriers so I will get back to that.
I agree! I definitely like the air unit model moreso in Civ 6 than in Civ 5, precisely due to Air Fighters being able to deploy to tiles. And even then I think that's not quite enough. What I've always really wanted are now considered hover units, like the hover units in Civ BE, or the airships in Empires of the Smoky Skies, or even how air units used to work in Civ 2 (or how air units work in AW lol).
I think having air units tethered to an Aerodrome/Airstrip is actually a supply and fuel abstraction. IIRC, back in Civ 2, air units could actually sit on tiles like regular units could, but if they stayed out too long w/out refueling, they'd crash. Assuming there were no other tile to land besides where they'd started from, that'd basically mean air units could at most spend half their maximum movement (rounded down) to go do something, then use the remaining movement to go back to where they started. The air unit model in Civ 6 is just enforcing the need to refuel, instead of letting air units crash. An air unit's real move range is double what their actual movement is; that's why an air unit's rebase range is double their movement.
By having carriers come with fighters, you can still do naval air assaults, just not bombing runs. Perhaps you could upgrade one that allows for bombers (super carrier). I'd also be okay with a carrier carrying land-based planes, but I don't think bombers need to be launched from carriers. I am not sure how to really model bombers in real life to the game so I can see why they let carriers carry bombers and stuff like that. But really, you will never see a plane like a B-52 on a ship, it's just too massive. They are refueled in the air. having mid-air refuels are one of the logistics challenges they face, but their range is also extremely far. So that's why I'd be okay with 'nerfing' bombers from carriers, especially if it enables the carrier to be more viable. I don't no what the proper fix would be to enable long range bombing runs, but they could certainly come up with something. Maybe allies can play a role in this (United States station their planes in foreign countries after all).
I kind of already answered this, but I wouldn't mind seeing Carriers come with their own Sea Planes or Air Fighters

And yes I also agree that Air Bombers are ridiculously strong in Civ 6.
To me, that actually sounds like an interesting challenge to overcome. Jet bombers in civ 6 are just way too good so being forced in the late game (when you are probably already snowballing) to adjust attack methodology would be interesting. I know that's not someone everyone would agree with, but it's quite common for people to wait until artillery for a big military push and the same for bombers. The reason is that it just makes it way to easy and the AI doesn't respond well. If the AI built in a remote location that you can't reach by rebasing, then maybe that gives you a reason to adjust to meet up to the challenge? Island hoping with many airstrips? I don't know, just a thought. A bit more punishing to the player who built the bombers, but a bit more rewarding when the plan is executed. Especially since you don't have an easy 'win more' button.
I like air units but also agree, I wouldn't mind seeing a bit of a nerf to Air Bombers, as long as that also comes with making walled cities a bit more approachable.