Frodo at Sammath Naur

[Lost One]

I think that, in the Letters at least (sorry, I don't have them to hand to quote), Tolkien is quite explicit that the choice is Frodo's. Exercising free will was a crucial thing for him. And if Frodo did not fail here, it seriously undermines his decision to leave Middle-earth: his unhealable wounds are not physical (or just physical), they are spiritual also. He knows he surrendered to the Ring at the last- understandably, given the pressure and situation, but still a choice.