"Disappeared" is a bit of hyperbole on my part... but effectively true.
No, entirely wrong.
They went from being confident enough to having the AGC+IMU+DAC auto-pilot the LM, including the maintaining of balance (via a 2-second update cycle, AFAIK) for a top-heavy LM
You keep on calling the LM top-heavy when it is one of the least top heavy items in the entire Apollo system. Yes, the centre of mass was above the centre of thrust, but that is true for literally ALL rocket systems.
Here's a fun thing for you to consider: Robert Goddard's early liquid fuelled rockets were based on the belief that a top heavy rocket would be difficult to control, so the rocket motor was at the top of a metal frame assembly with the fuel tanks below, putting the centre of mass well below the centre of thrust. And then some experiments proved that a rocket works just as well with the engines right at the bottom. And this was literally a hundred years ago. Your concept of 'balancing' a rocket on its thrust has been known to be wrong for a century at least.
And I gather you believe a '2-second update cycle' in some way means it takes 2 seconds to respond to an input? Otherwise what has this to do with anything?
For the LM, they didn't even bother to create a POC (Proof of Concept) to show this trio in action
LM-1 was the concept. It flew on Apollo 5, uncrewed, and it worked. Can you think of a better way to prove the system works than putting it in the actual spacecraft it is designed to operate and flying it in the environment it is supposed to operate in?
And that 'designed to operate' part is significant. You can't just chuck the same computer with the same software in a completely different vehicle and expect it to perform. And after 20 years of dealing with people making such claims as yours I feel pretty confident in saying if they
had done as you suggested, hoax believers would call it an invalid test because it's not flying the same vehicle in space as they said it could.
The absence of a POC for this trio, prior to doing the singular "on mission field test with A10"
Nope, not even close. The LM was flown, with the AGC, on Apollo 5, 9 and 10, and Apollo 11 WAS the final test. The issue is not an absence of POC, it's an absence of what you think POC should involve, which carries no weight whatsoever.
Why did NG throw out most of the docs for the LM? (unless they didn't want people digging it up later to see that the appropriate amount of work/test/validation/design wasn't actually workable).
Because, as with many companies, they were not making it any more, and the vast majority of those documents are very specific construction plans that they don't need any more and can't justify the storage space for decades later when they have active projects with a higher call on the available resource. There is still a huge amount of published documentation about the LM and every other aspect of Apollo.
Why get rid of all Telemetry tapes, unless you are hiding the fact that this data may not have existed, or that the data on these tapes didn't fully make sense, etc.
Or that it's just of no use any more, and in any case the particular data format requires machinery that isn't made any more to read it. Why did I chuck out my entire VHS collection when my last VHS player broke and I can't get a new one any more?
Once again, the problem here is squarely your inability to conceive that people and organisations don't have to work the way you think they should, that your ideas are not always right, that your experience in no way makes you an expert in Apollo or space flight of any kind.