What is interesting to me about the way Tolkien represents heroism (in Frodo's
case) is that here we have a failed, "modern" hero who nonetheless is, as you
point out, given the traditional accolades in the end. The literary
parallels and contrasts are quite interesting here. I am painting with an
extremely broad brush, so I'll sweep over finer details and make some hasty
generalizations. :-)
Among Tolkien's contemporaries there were the different camps on the theme of
heroism: on the one hand, there were those who brought heroism into
question or who saw the War and the cultural decline accompanying it as signs
of the decay of Western civilization (I think of the World War I poets here,
and the early T.S. Eliot, for example), and then on the other there were those
who retreated into a kind of recreated mythic heroism (think of T.E. Lawrence's
heroic self-representation in Seven Pillars of Wisdom). Tolkien,
it seems, stands somewhere between the two extremes, though he reinvents the
modernist's critique of the hero and sets him alongside Aragon, the Lawrence of
Arabia hero with a destiny he is living out. By making Frodo a hero
despite his failure, Tolkien is in line with some of the other writers of the
first half of the twentieth-century who saw the hero as an Everyman faced with
adversity. Like Sam says in "The Stairs of Cirith Ungol," the hero is
really the ordinary Joe who winds up in extraordinary circumstances, but then
goes home to dinner after his deeds are accomplished. This is a very
twentieth-century kind of hero, like James Joyce's ordinary
heroes.

Howe, Drowning of Númenor