ITA with Val's post, by the way.
Honestly, the "allows study of more advanced topics" thing makes no sense to me unless one assumes that there is a finite shelf-life to learning math and science topics. As far as I can tell, there isn't.
Acceleration allows students to reach advanced topics EARLIER. The question is whether or not that is a good goal. I'd say that as a side-effect of natural learning and meeting an individual's needs and interests, it's fine-- but probably not a good thing to have as a primary GOAL, so much.
But that's me.
I see the need for acceleration as being most important for polymaths who have multiple future avenues of study. Per Bostonian's point, if a student is potentially interested in a field that requires higher level math to access more than a conceptually basic understanding of the subject (e.g. finance, economics) then I do think math acceleration is warranted. Granted, most of our children will see the need for the math in their field(s) of interest and be intrinsically motivated to learn it, too, so the acceleration will be needs-driven.
Really, in many fields, you have to be at least at the senior undergraduate level in the topic before you have a realistic understanding of your interest in, and willingness to continue in, studying the topic.
I think all students would benefit from the topics Dude and Zen Scanner mention. Ideally, elementary math courses would incorporate proofs and logic as early as possible. To be an effective critical thinker requires a deep meta knowledge, and I think that is largely lacking in modern math instruction. (It's also why I'm keen on the idea of AOPS.)
And I agree with your critical seagull scaffold hypothesis for autodidacts to take flight. (Terrible pun!)
