I think this section develops Frodo and Aragorn; we learn why Aragorn's going to make a great king before we learn that he's going to be a king at all. And Frodo bearing that wound for all those days... well, I'm sorry Jackson cut it out of the movie. Especially when they reach the Ford and Frodo gives that one last act of defiance...."By Elbereth and Luthien the Fair, you shall have neither the ring nor me!" Sorta makes that whole "If you want him, come and claim him" bit seem silly, doesn't it?
Yes it does! I wish the movie hadn't changed that, especially since they didn't do the barrow downs part. The movie audience never got to see much of Frodo being "made of sterner stuff."