No, the notion of one wanderer reaching the Swiss Alps isn’t too bizarre at all. The notion of an entire civilization pouring their creative energies into reproducing something only he had seen... that’s what’s far fetched. And your notion that it could be true, therefore it is true is what I’m criticizing. You’ve strung together an immesibly long cascade of immensely improbably things to support your argument of what you say did happen. Not everything with a pinched neck (”sphinctus”) is a mushroom.
I am sure the Egyptians understood the general nature of the shape of a mushroom.
Now, regarding what may have been the original and far smaller focus of interest at the site of what is now the Sphinx, that would have been there all through the Ice Age for 80,000 years before the Egyptian civilization grew up.
These are called Sandstone Pillars. They are in the Sahara somewhere. I particularly like the morel shape of the first one in the line, and if you look up to the right you see a couple more with "heads" typical of a mushroom fruiting body.
Most likely any such forms along the Nile Valley would have early on been identified as objects of veneration by the hunter/gatherers who traveled there for TENS OF THOUSANDS OF YEARS.
The tourism company that takes you past these honeys in Egypt's Western Desert calls them "sandstone mushrooms" in fact. Definitely something to attract both neolithic, new neolithic, and maybe even paleolithic and modern interest.
(People pay good money to see these things and you doubt they existed? I'm more concerned with why the Egyptians decided to quarry away the stone UNDER one of them.)