Darkness or Light? Philosophy in Knights of the Old Republic.

But the fact remains: if Anakin had been unconscious and Obi-Wan was fighting Dooku, I'm 100% sure Obi-Wan would have spared him... And if he had spared him, it's quite possible he would have revealed the truth about Palpatine.

If Obi-Wan had been fighting, Dooku would have simply killed him. He may have had an order from Palpatine to provoke Anakin, but not to kill him. Moreover, Anakin was already stronger than Obi-Wan, but he lost at the end of the film in a rather illogical way, probably because he succumbed to rage and lost self-control, which is fatal for any fighter.
In general, while watching the 3rd film, two questions arose: what is so bad about the Sith, and why are the Jedi so stupid? Although the second is more or less clear; they are used to using the Force for precognition, but they were not taught to use their brains. As soon as the Dark Side closed the easy path to the future for them, the Jedi became like blind kittens.
Because if Anakin had known about the possibility of using his brain, and not just his spine, he would have asked himself questions like: why does a young, healthy woman die during childbirth in the age of mega-medicine, who is the Sith who controls the Senate, is it worth believing the fairy tale about Darth Plagueis the Wise, etc. If he had thought about even a few such questions rationally, he would have saved his wife, brought peace to the Republic, and restored the balance of the Force a quarter of a century earlier. He would have lived peacefully and happily on Naboo, and when he had gained enough Jedi strength (and sooner or later, with this scenario, he would have surpassed even Cheburashka Visarionovich), the Council would have crawled to him, because they understood only the Force and nothing else.