Nah you guys don’t get it. For all that Gandalf complained about Pippin, he better than anyone else knew that Pippin was absolutely crucial. Pippin accomplishes a very impressive feat: not only does he manage to see something in the palantír (most hobbits would perceive nothing, as these stones were designed for use by high elves), but he manages to close his mind against Sauron. That is a seriously impressive feat of ósanwë given Pippin’s youth and almost total inexperience. The only clue Sauron manages to glean from the meeting with Pippin is that he is in Meduseld: which Pippin probably did not even directly give to him. Pippin did not tell Sauron his name, so Sauron is led to believe that Pippin is Frodo. I remind you, in the books, the Good Guys manage to trick Sauron, by making him believe that Aragorn has claimed the One Ring. They can only do that because of Pippin’s ridiculous feat of ósanwë. Far from sabotaging the mission, he is the one who allows it to succeed (albeit, not on purpose). This is why Sauron doesn’t think anything is fishy when Aragorn wins the Battle of the Pelennor Fields by controlling ghosts: that would be consistent with the idea that he is using the One Ring. Which Sauron believes that Pippin brought to him. This is why Sauron pulls out his old “play nice and weak” card from his Númenor days. He first of all believes that Aragorn is a lot more powerful than he actually is, and secondly thinks that the Ring is beginning to affect him.
He should perhaps have remembered that Aragorn is named for Fingolfin. Fingolfin’s mother-name, Arakáno, would properly be translated to Sindarin as “Aragorn”. Most people would not show up to an enemy fortress with an army they knew was far too small, and start a battle they knew they would lose. But Fingolfin famously did exactly that.
When you read the line “fool of a Took!” It is important to understand that in the context of Gandalf calling himself a fool on several occasions. Galadriel too sees beyond the veneer of foolish naivety in Pippin. She gives him and Merry belts that almost definitely were once her brothers’. A golden flower on a gift from Galadriel can only be a golden lily, the sigil of the House of Finarfin. Galadriel, while all hell was breaking loose in Tirion, raided her brothers’ rooms and took their belts from when they were little kiddos, hauled them across the Helcaraxë, and then held onto them for three Ages before giving them to two hobbits she just met. Merry, of course, is comparable to Angrod and Aegnor: his great deed is done in a moment of beserk rage, and it is a feat of strength. This then implies that she is comparing Pippin to Finrod. That’s one hell of a complement coming from Galadriel: but as I just pointed out, entirely warranted. Pippin manages to reproduce Finrod’s feat of radio silence, in the face of torture by Sauron. Which again, is extremely impressive given that Pippin is far younger and less experienced than Finrod was.