[dancing spawn of ungoliant]

Who would then have taken the Ring ? Merry or Pippin...err, nope, Aragorn wouldn't have trusted them in such a big thing (well, that's only my opinion!).Sam wouldn't have taken the Ring when his master was still alive and Aragorn maybe scared the power of the Ring just like Gandalf did.
And then, was Frodo so attached the Ring that he would even have given it away!?

In the book Frodo's fading isn't so fast - it's overdramatic in the movie. So maybe there wasn't such a hurry to take the Ring away from him.