I agree that the US' capacity to assist the UK on the ground and in the air would have been limited, but the US had either the second-most powerful or most powerful navy in the world at the time (I'm not sure when they became top dog - I suspect with the ship building program replacements post-Midway, but they were still extremely powerful). If, in the very unlikely event, Germany had managed to damage the RN enough to allow Sealion in the first place, they could find themselves on the wrong end of the USN smashing up their beachheads (which is by far the greatest assistance they could provide in any event).
I think we are close to an agreement ... The problem for a US intervention (send the fleet) is timing. While the Navy was much more operationally competent than the Army in 1940 and 41 they really weren't a quick reaction force. So for example, the Germans kick off Sea Lion and after a couple of days the US gets news that things aren't going well for the Brits (the Germans make a few landings and are not thrown back into the sea immediately and oh by the way half the Royal Navy seems to be sunk trying to close the Channel which remains open to German resupply and reinforcement operations. The US then presumably declares war on Germany and dispatches a couple of battleship cruiser task forces and say 2 of the 4 carriers it has. It then take 10 days to cross the Atlantic and you have to refuel the fleet (something the Brits could do certainly) and then send it into the channel where it gets to take on the Luftwaffe which although they weren't great at anti ship in 1940-41 (or more correctly up to Japanese standards) they were pretty good (see Crete) and oh by the way they just managed to cripple the RN the week before so they are getting better. It also helps that the Luftwaffe has multiple bases along the French side of the channel so carrier strikes from ~150 carrier planes (technically inferior to Messerschmidts and Stukas) could knock out their bases. Sending a fleet into "narrow" waters controlled by hostile air is a recipe for disaster.
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