My twins took the SAT when they were 12yo (they are now 16yo). Although curiosity was definitely a factor, our main reason for signing them up (we went through NUMATS) was to qualify for online courses through the Northwestern University Center for Talent Development (CTD). Our kids did take several online courses through CTD to augment a sometimes lackluster curriculum at their public middle school. Although the online courses were a bit pricey, they were way less expensive and logistically more convenient than the alternative (gifted private school). We generally had good experiences with the online courses, and they gave the kids an opportunity to pursue in depth some topics they wouldn't have otherwise.
In hindsight, I think it would have been worthwhile to have the scores just for the curiosity aspect. Although we never pursued DYS or SET, both kids had scores high enough to qualify. And, although we always knew our kids were smart, seeing the scores has added to our confidence as parents in encouraging and supporting our kids' ambitious goals.
