Hitler never seriously intended to invade England - not because he was afraid of the navy, but because until his dying days in the Fuhrerbunker he believed his Aryan Brothers across the channel would leave the Allies and join him. He was surprised they declared war (France and England declared war on Germany, not the other way around as many people think); he was surprised they didn't join him after Dunkirk and the fall of France. Hitler was easily surprised.
In Spring 1940, the German navy had 0 aircraft carriers; 0 battleships; 2 cruisers; 2 pocket battleships; 2 heavy cruisers; 4 light cruisers; and ZERO landing craft (as well as assorted smaller craft) - and it wasn't because they'd all been sunk, they hadn't been built. Does this sound like a navy preparing for an invasion?
In Spring 1940 the Luftwaffe had 0 heavy bombers; 0 torpedo bombers; and 0 long-range bombers (and none in development). Does this sound like an air force preparing for an invasion?
Regarding the importance of the British Navy as a deterrent, just because "Churchill and almost everyone in Britain knew this cause almost the only thing important to them was maintaining the navy" doesn't make it true - and I'm a Churchill fan (with the benefit of hindsight).
Hitler's plan was that through military attrition ("The Battle of Britain") and a naval blockade - the U-Boat war, which the Royal Navy was losing in astronomical numbers - England would eventually see the light and join them in their crusade against Communism and Stalin. Germany could have built a surface fleet capable of clearing the Channel enough to secure an invasion but chose not to - they had the resources, but they allocated them elsewhere (the U-Boat campaign being notable).
And to end, as you did, on a baseball note: Harry Frazee was a Broadway producer first, a baseball owner second. "No No Nanette" was a smash hit, still playing worldwide in revivals to this day. Who's to say he didn't think he came out ahead in the trade - and who are we to tell him he didn't?