I enjoyed this tremendously, even though the theory you are debunking is tremendously stupid.
The alternative ending is puerile and anile. It lacks dramatic interest. The end of LoTR is so grueling precisely because Sam and Frodo have given up any expectation of surviving the experience. They get past the point of being able to struggle or plan and simply endure — but it’s that endurance, and greed (Gollum’s) and just dumb luck that wins the day, not the avian air cavalry.
The book ends when the Ring goes into the fire — the rest is necessary to tie up loose ends. The Eagles in particular are necessary because if Frodo and Sam were actually roasted, it would make it too depressing for children or really anyone, and they’re a very light way to resolve this loose end — “The Eagles are coming!” and Frodo wakes up in bed.
Frodo suffers permanent loss but still lives to tell the story — it would be too awful any other way.
Finally, the interpretation of “Fly, you fools!” as literally “flying” has to be the dumbest, er, stuff I’ve heard in a long time. As you say, it’s inconceivable that the blunt Gandalf would use his last words for some obscure riddle. If he meant eagles, he’d shout, “Eagles!”
The actual meaning is typically Gandalf — “What are you doing standing around gawping? Get out of there, idiots!”
Thanks for a fun article!