I think becoming interested in more stuff would be a necessity for anyone with immortality. Otherwise you'd be miserable.

Right; but the people who are interested in One Thing or Nothing just say "I don't think I'd want to be immortal; it would get too boring."

I would challenge that you can group people into those three categories. I'm interested in everything from quantum physics to category theory to python, but I have zero interest in basket-weaving techniques of the 18th century.