I ran some tests as Germany last night to see if there was a way to exploit land based air to get SAGs into effective firing range of CVs. The results were basically what I thought they would be.
I tested 3 basic fleet compositions. CA/CL "cruizerg" fleet, a BC/DD fleet, and a BB/CL fleet (for more AA). All fighting took place either in the Channel or at the mouth of the Thames. Battles took place in early/middle 1940 after the Fall of France with some combats in 1942 against the USN off the coast of Morocco.
1) Cruizerg: The CAs did manage to sink a significant amount of older RN ships. With land based fighter coverage, the RN's CAGs spent a lot of time being shredded. But the moment the RN brought more modern ships into the fight, the CAs died. They never got into range of CVs even with INTs sweeping the sky of CAGs. The CAs simply don't have the hull or firepower to survive surface engagements against even mediocre modern BBs. The German Navy failed to survive long enough for the USA to enter the war.
2) BC/DD: They trashed a lot of RN ships. With 1938 capital ship armament, they were smacking the RN around fairly well. The CTFs would come out to play and the Luftwaffe would shred the CAGs. But the BCs simply could not get in range to do any significant damage. As the RN got newer ships, the BCs started spending more and more time in port getting repairs. The lower hull values meant that, while they weren't dying off in droves, their operational time was much reduced. They really did not spend much time playing with the USN off the coast of Morocco, staying port almost half the time due to excessive battle damage.
3) BB/CL: I tech rushed all the way to H-class BBs before building any. While not as fast as BCs, the speed difference was smaller and these H-class BBs had much more hull than the BCs. They completely dominated all RN SAGs they encountered, claiming 65% or so of the RN's BBs (the Italians got the rest in the Med for once). The fleet spent almost 9 months operating within sight of Dover before finally returning to port. Battles against RN SAGs saw the RN get completely owned. Battles against CTFs resulted in no significant damage to CVs. Interestingly, looking at the battles in the window, it was the BBs who got closest to being in firing range of the CVs, not the BCs. They still failed to get into range, but there were some times that they started close (did they just get lucky? something I missed in the battle? Leader effects I don't understand?). Battles against CTFs were victories because the CAGs would be shredded and the CTF would flee the sea zone. Mixed battles still saw CVs running away while the BBs would just hammer the BBs and BCs (I suspect that with plenty of targets to shoot at, the BBs were just ignoring the CVs completely to focus on targets they could reasonably hurt).
What was most interesting about the BB test was that the BBs kept the ocean effectively clear of CTFs (until the US entered the war). We didn't kill any, but the CTFs spent a large portion of the war sitting in port with no screens and dead CAGs. While that's not the same thing as winning at Midway, operationally, it's just as good from the German standpoint. With the RN suppressed (which could not have happened historically), it's not gamey to launch Sealion anymore.
When the USN entered the war and obliged me by landing in North Africa, the BB based SAG performed poorly against USN Death Stars. I didn't lose any BBs (in fact, we killed two prides of the fleet in two weeks), but they simply got shot up too badly to stay on station for very long even under friendly fighter cover from Gibraltar. I'm not sure if it's because of excessive CAGs, or because I should have put more wings at Gibraltar, or if it was the difference between RN tech and USN tech (let's face it, the USN had could be ahead 1 level in all relevant categories without even breaking the ahead of time penalty by the time we were fighting each other), but even with friendly air cover, the BBs found life really difficult.
The Torch landings didn't make a difference in the overall war on way or the other because the USN could still throw a Death Star or two against me and still find the time to invade Okinawa.
An interesting effect of these combats in 40 and 42: the BBs sometimes had to take a break in port while waiting for new CLs to get produced because we lost enough screens to incur the inadequate screen penalty. We would lose screens sometimes and I didn't budget for a lot of extras. With hindsight, I should have built a few more earlier in the war and they could have stayed on station even longer.
Another interesting tidbit: The starting subs for Germany were able to continuously raid convoys in the North Atlantic until the USN entered the war. The H-class BBs operating off the coast of southern England tied up so much of the RN's resources that it couldn't spare the ships to hunt down 3 lousy subs. Had I known this ahead of time, I might have built a few more and made them more advanced.
My verdict:
1) SAGs will never bag a CV no matter how much land based air cover they have. Bismark, Yamato, Marat, and Royal Oak will never have the coveted "killed CV" entry in the ledger.
2) SAGs CAN effectively suppress enemy CTFs if they have lots of land based air cover. USN Death Stars might just require excessive air power that even Germany can't afford (either to physically throw in combat or to supply in theaters outside Europe).
3) A suppressed CTF is not as fun as sinking a CTF, but it is just as good IF you are Germany and IF you are trying to achieve specific naval goals (primarily Sealion and maybe taking the Suez/Bombay to knock them out of the war). Italy can get some mileage out of this in the Med. Japan cannot afford this luxury against the USN because the USN can afford to repair 30 CAGs at one time while building 30 more. CVs that are not dead are CVs that will bring another crate full of naval air power to the table in 3 months.
4) BBs have a perfectly valid place in naval OOBs for major powers excluding anyone intending to attack the US. If you are a major power that already has decent BB practical, you are not Japan planning to attack the US, and you have plenty of air bases (or potential air bases) within range of enemy naval targets, then build BBs. Just don't try to project naval power to Hawaii or Baltimore.
4a) The Soviets are so behind that they might as well go the CV route, but because Vladivostock is in range of most of Japan, up to date Soviet BBs could still seriously threaten the IJN at home. What is the IJN going to do? Fly 12 CAGs against 30 INTs based in Pacific? It's not like the Soviets can't afford excessive land based air power.
5) Do not antagonize the USA. Death Stars are bad for your health.
EDIT:
I forgot number 6: Air power is decisive in naval battles. Period. No exceptions. Seriously, I meant it. But CVs are not required when fighting near the coast, so just make sure air power is present.