And I agree that Strider's "if by my life, or death, I can save you I will" - Is much stronger in Rivendell than it would have been at Bree.
And in my further reading tonight, I am nursing a theory that when Aragorn joins the company, that is when Frodo begins to begins to show leadership, because Aragorn treats him that way. And, perhaps, following Aragorn gives him confidence and security that he has not felt since they started, alone and guideless in the wild.
Aye ... we all start as such ... and know the the need of a valiant guide.
... (and protector) which does not happen for everyone.