I find this moment very interesting not just because of the Oath of Fëanor but because of what it says about oaths in general.
Because imagine that all of the Fellowship did swear to go with Frodo to Mount Doom. Legolas, Gimli, and Aragorn would have felt obligated to abandon Merry and Pippin to the orcs to go with Frodo; who knows how the Ring could have used that guilt to twist them. Gollum would never have had the same dynamic with Frodo, because he hated Aragorn. Gollum wouldn’t have been at Mount Doom to destroy the Ring. Aragorn wouldn’t have been there to take the Paths of the Dead. Minas Tirith would have fallen. There would have been no march on the Black Gate that cleared a path to Mount Doom by distracting Sauron.
“No oaths,” means: the world is larger and more complex than you know. You don’t know that the thing you’re swearing to do will turn out to be the right thing, the best thing, in every possible circumstance. Have the humility to recognize that complexity.