You have completely missed Gandalf’s motivation for sending Frodo on with the One Ring, and why Frodo was successful in the end. Gandalf is an angelic being who kept his faith with Eru Ilúvatar. He was aware of the seeming impossibility of the task, and that it would only be accomplished through the grace of a higher power.
The improbable absurdity of the One Ring dropping into the hands of hobbits, of all people, suggested to Gandalf the ineffable hand of Eru Ilúvatar. He didn’t send Frodo off to certain doom because he had no other options; he sent Frodo off to what seemed like certain doom because he had faith it would somehow work out.
Gandalf does not operate on cold pure logic like some sort of robot Vulcan; he’s a being of faith.
The first is that Bilbo was capable (with, admittedly, much cajoling) of handing over the Ring to Frodo. Given that the Ring is addictiveness personified, and fully capable of twisting every decent human impulse to justify selfishness (specifically, possesiveness concerning itself), that was no mean feat - it shows that it was at least possible to defy the ring to that exent. Admittedly, though, this was Bilbo and not Frodo.
The first example specific to Frodo, that showed he had a strong will and was able to defy the ring, was when he offered to hand it over to Galadriel. Again, the possessive/addictive nature of ring ownership would be working against this.
The second example deals with Frodo’s strength of will specifically - for example, his pivotal decision to leave the company of his powerful friends and strike out for Mordor on his own. This was of course virtually suicide on his part. It demonstrated that he was placing the outcome of his quest ahead of his own survival - a decision that would take great strength of will to make.
Perhaps you are right, if one knows the entire lengedarium.
It is only fair to add that a casual reader of the book would not of necessity understand these mythological underpinnings. In the book at least Gandalf appears to, at times, suffer from doubts and worries just like a human, even though he isn’t one.
I was watching PJ’s Two Towers last night and got out the book to sort of follow along. I didn’t realize how much of the dialog in the movie was lifted directly out of the book. It’s often given to different characters and sometimes rearranged but I think that says something good about Tolkien’s ear for prose.