I disagree. Partly because your not talking just a couple of carriers. The combined US and British navies could have put around 20 aircraft carriers into service giving them around 1,000 aircraft which is a pretty big CAP. Long range aircraft flying from the UK like the P51 Mustang and the P38 Lightning, could reach Into Germany and would have had no problem covering many bases located in France. Also once they take Jutland or the rest of Denmark they could have used those land bases.
But the logistical nightmare that would come with trying to support 20 carriers outweigh any benefits. The longer and more complicated supply lines, risk of bad weather, risk of enemy action and generally less -capable naval fighters are all good reasons to avoid this plan.
Not to mention that 1000 planes isnt actually that many in the scheme of things. At the beginning of June the 2nd TAF had over 1300 aircraft alone, and that doesnt include US planes which will easily add another 50-60 squadrons of fighters alone before you get to the other aircraft.
Final point is that to do this the allies would have had to strip pretty much all their carriers from the pacific theatre, leaving their forces over there without significant mobile air support. That sounds like a huge and unjustifiable risk given that the allies had a massive and unsinkable carrier they could use instead (Britain)