Frodo Baggins is not a hero - at least the movie version of the character. Sure, he makes a big stink about what a "burden" the ring is, and how it's "His task" and "No one can help him." He also vilifies Gollum for pursuing the ring, and Sam for offering to help carry it. Frodo has been charged with the task of destroying it.
Not only is he a liar, treats his friends poorly, and betrays the trust of his captive; he also accepts unwarranted credit for completing the task of destroying the ring. It would be the equivalent of having someone else take your final exam for you, and you claiming the grade as your own.
Once they finally get into Mount Doom, mostly thanks to Sam's tenacity and unshakable spirit, not to mention some form of idolism or maybe Stockholm syndrome; Frodo fails. He fails repeatedly. He succumbs to the power of the ring, and the ring never would have been destroyed if Gollum hadn't bitten his finger off during the fight over the ring. Even once the ring was off, Frodo fought to gain it back, but again, not to destroy but to possess. There is no hero in Mount Doom, other than maybe the mountain itself. The ring was destroyed by an accident, not by intent.
Frodo is an imposter. If anything, Sam stays the most honest, and absolutely deserves some credit. Frodo was just lucky.