This is what I meant by the Germans voluntarily switched targets. There isn't a counterfactual here unless your counterfactual argument is "What if Hitler wasn't so bat shit insane, even though said insanity was integral to him"
Again, the UK had the option of withdrawing their fighters and pilots out of reach of German raids, in exchange for leaving their population centers less well defended. As Germany's experience demonstrates, this would have been a sustainable strategy for the UK in terms of staying in the war.
I'm knocking Churchill's works as a historical overview. They are incredibly valuable as a memoir and primary source. But what makes they valuable primary sources is also what makes them incomplete or flawed historical works: lack of access to German, US and USSR archives and the author's biases. In the case of the latter, Churchill frequently implicitly and explicitly shapes his writings to portray himself favorably or otherwise color a story to fit the narrative he wants to present readers.
The success of the invasion would have mostly boiled down to four things.
1. Could Germany neutralize the Home Fleet?
2. Could Germany neutralize the RAF?
3. Did Germany have enough sealift capacity for a large enough first day invasion force?
4. Did Germany have enough capacity to supply an invasion force in heavy combat?
The answer to every single one of these questions is a resounding No, and mind you, the a "no" to any of these questions would have guaranteed German failure. I really don't you think grasp how much of a feat an amphibious invasion is and what it requires of a country and its military.
Churchill frequently refers to writings from the Enemy, so I think there there is plenty of balance. But obviously, yes, it's his perspective, and the inclusion of writings from the Enemy are used to specifically weigh up the prevailing thoughts at the time, and whether they were right in their assumptions or not - and many of the time, Churchill and the government were not correct in those assumptions, as I'm sure you can imagine.
Anyway.
What is not in doubt is the RAF was taking a hammering in South and South East Britain. If Germany had persevered, the RAF would have been hugely ineffective. So the answer to 2 is not a resounding
no, unless the question is 2. DID Germany neutralize the RAF - no it did not. Could it have done? Absolutely it could have done. Churchill was only too aware that he was looking at rookies with potentially ruined operations and communications. They would have been fodder.
The British army had already lost the Battle of France and should have been routed but for a miracle at Dunkirk. Churchill was already teetering on a negotiated peace earlier that same year. The RAF was then taking a battering before Goering (not Hitler) starting making unforced errors. Hitler then made the biggest one of the lot - USSR.
Britain was let off the hook. It survived, replete with its RAF.
Actually, when I read your posts back, I notice you're not really saying a whole lot different other than that you are adamant Germany couldn't have invaded Britain. I'm saying it could have if it had won air superiority, which it was on its way to achieving, but how successful it would have been beyond that is uncertain. Britain was actively expecting them to try it, which is a far cry from 'no possible way'. There's a question about how effective the Luftwaffe would have been against the Royal Navy even if the RAF was rendered ineffectual. The whole thing could have been an unmitigated disaster if Germany had tried it, but we just don't know. What we do know is Britain had faced numerous defeats against Nazi Germany, and had been absolutely embarrassed alongside its allies in the Battle of France in a matter of weeks in what should have been an evenly pitched battle.
Weeks. It was a demolition job.
I won't be taking anything for granted about what Nazi Germany could or could not have done. I've no doubt if the Battle of France hadn't played out like it had, people would be arguing that couldn't possibly have happened either. It wasn't just possible, the rout was real.