why Frodo?

[Iris Alantiel]

If Sam had been the one to bear the ring, his motivations would have been to save Middle Earth. To save the Shire and Rosie and all of that. But maybe Frodo had the slightly personal quest; he had seen the effect of the ring on Bilbo, and the effect it was starting to have on him, and he felt that he had to destroy it to save himself.

But if Sam had been the one to bear the ring, wouldn't he have felt its effects and needed to save himself? Wouldn't it have become more personal for him? It might have started out as a labour of love for ME, but wouldn't it develop into a quest for personal salvation as he saw the ring beginning to take over?