Analyzing Frodo based on the ending of Return of the King misses the full allegory of who he is.
His strength is not defined in his brawn, intelligence, etc but rather his smallness and willingness to accept the burden of the ring. Others "more capable than he" fell victim to his power multiple times (eg Boromir). His smallness is intentional to show that even the smallest and most unsuspecting people in the world can have a profound change.
In the same way, Gollum is left alive when he could've been slain multiple times to show the value of life and the importance of mercy even when it cannot be seen.
Sam is meant to demonstrate the importance of not fighting sin on our own. You are correct in saying that he shoulders a large load throughout the journey and ultimately helps prevent Frodo from keeping the ring. Yet how often to we as humans fall short when faced with addiction and other vices if we rely only on ourselves and not the people around us? Bringing the burden of sin into the light and calling on friends and family will always help us defeat it. Frodo would've have failed without Sam, however, do not think that Sam would've been able to complete the journey he himself, he too would've fallen without Frodo.
The work is a direct relationship to our weakness in the face of sin and is inherently pro-life to the maximum. It calls us to seek refuge from the burden of Satan in our friends and family, take up our cross daily with meek and humbleness of heart, and have mercy on even the most outcast among us
Edit to add: yeah I'm a Christian nerd and I love LOTR