The group probably saw no real need to take the ring from Frodo, since he wasn't that weak. Sure, he was fading, but he was strong enough to walk, talk and bear the ring (In the book, he wasn't so delirious and helpless as he appeared in the movie). Besides that, I don't think any of them would have been willing to take it. If Aragorn wanted to bear it, he would have taken the ring from the hobbit the moment they left Bree.
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The only thing necessary for the triumph of evil is for good men to do nothing.
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