How much range do you think they need? Those carrier groups will need to go through those straits, to be in position to defend the beachhead (Unless you are seriously planning to force them to overfly the Danish Peninsula on every single mission

). Once there, they can be cut off by five German sea scouts with a rowboat. ASW has never been an exact science, but in the Baltic, during WW II? Unjustifiable risk doesn't even begin to cover it.
Actually Baltic sea during Second World War was a environment where subs were greatly at risk, as displayed by failed Soviet and German sub campaigns there. Even during WW I with British subs it was not an easy ground. Only with introduction of Type XXIII clones it has become better for subs. Narrow waterways also made it possible to use some quite extraordinary measures, such as controlled minefields and asw-nets (which in OTL succeeded closing the Gulf of Finland for almost two years) etc.
Danish straits area is very shallow, even more difficult for subs than English Channel in which the German sub campaign against Overlord Fleet was not a great success.
In WW II those carriers will need to be within 100 miles of the beach, although it would be better to be 50 or less. The fighters & fighter bombers need to be able to loiter in support. Unlike today there's no air-to-air refueling, so the need will always be to rotate planes into and out of the combat zone. The USN would have to carpet the Baltic with carriers to make this work. Even then you are counting on decent flying weather in a part of the world that is not exactly known as a sun drenched paradise.
Even, say 100 miles range does not require carriers to enter Baltic, just the area between Gothenburg and Jutland. Sjaelland and Lolland are quite ideal places to construct airfields for follow-up operations. Also, in difference to the operations in the Pacific the UK would be very close to replenish carriers, which could mean, I would imagine, that carriers could be deployed with aircraft overstrength.
BTW: The Germans regularly used to hit the 8th AF formations with 1000+ fighters, well into 1944. That is the entire fighter force from 17 Essex class ships (2 squadrons of 36 planes each AFTER the Kamakazi threat forced the Navy to increase the fighter force on each carrier by 50%). The 17th Essex wasn't commissioned until November of 1945 (six months after VE Day).
Luftwaffe was already broken before summer of 1944. And, who says that carriers would have to operate anything but fighters (excluding small number of Avengers and Swordfishes for ASW patrol)? If we put air strength requirement for, say, 1500 planes (with ready resupply from British isles doable), this would require, in June 1944 terms, the following carrier air power:
RN Fleet carriers available:
HMS Implacable and Indefatigable - 140 planes total
HMS Furious - 50 planes total
HMS Illustrious class - 220 planes total
Total of 410 planes
RN Escort carriers available:
23 Attacker class - total of 552 planes
RN total strength: 962 planes
USN requirement is thus some 600 planes, doable with USS Ranger (86 planes) and some 20 Casablanca -class escort carriers. USS Saratoga was also not deployed in crucial operations, able to carry some 90 aircraft.
Even when rounds up the requirements, it's still doable with not much carriers taken from PTO. Escort carriers for convoys would have to be ripped off, but then, an invasion and campaign on Baltic and North Germany would end the German U-boat threat in very quick order.
This plan also requires the U.S. to effectively abandon the Pacific to the Japanese. Hawaii would be held, and Australia was, in reality, too big of a bite for the IJA, although taking Darwin can not be ruled out. The U.S. then has to fight all the way acrosss the Pacific AFTER VE day, stretching the War well into 1947. All this to end the European War a few months earlier, assuming that everything goes exactly as it is envisioned. If not, then the Western Allies lose an entire Army Group in a greatly expanded Market Garden style disaster.
With more exact thinking, no I don't think this would require abandonment of Pacific Campaign, though perhaps elimination of dual SW Pac - Central Pac campaign and merging them to a single campaign. Marianas could be taken, but Philippines could be iffy.
As for potential gains, they're quite numerous:
- Elimination of German sub threat in very quick order
- Bonus targets in military sense. Campaign on German soil is much more effective than one in French soil as every bridge span dropped by airpower and every village occupied directly makes effect on German war production.
- Political significance. Attack on Germany direct takes away the motivation of German generals, some of whom justified fighting the Western Allies because of the need to keep Soviets away from German soil.
- Most importantly, looking from just US figures, less Allied casualties. Casualties from ETO were gigantic compared to those of PTO. Not as much French, Dutch or Belgian collateral casualties (although Danish casualties would ensue, they would be less).
- Significant post-war gains, perhaps even an Eastern Europe in Allied hands. With Western Europe not having gone through fighting significantly less need of US economic aid. Germany would be rubble anyway, so no change there.
But I agree, a campaign plan suggested during WW II like this would have been a no-go. The planning process for Overlord was so cumbersome that there's no way that invasion of France would have been swapped for any operation. In Pacific, where there seems to have been less interference, commanders such as Nimitz were able to take risks and change objectives more freely.
You are right in that the U.S. puts carriers into the Gulf, and scares the piss out of itself every time. Those ships are hellishly vulnerable there, despite the fact that they are defended a hundred times better than TF 58 was on her best day during WW II.
Yes, I think that those deployments are made because of the most severe threat to the USN carriers, the USAF...
EDIT:
But let's continue this Baltic speculation: After initial landings on Northern Jutland and Sjaelland the follow-up landing will be much easier, as the distance between Sjaelland and Lolland and German proper is just between 10-30nm's, with much easier weather conditions than in English Channel. Baltic also has negligible tides. Thus, instead of Normandy armada just tactical landing craft will do.