Is there any particular reason to do this other than:

1) to enroll in Duke TIP (they seem to have some nice programs, but it's not needed by us at this time);
2) to advocate (also not needed);
3) for bragging rights/to get recognition? (also not needed)

DD is a good standardized test taker, but she is not a math genius, nor is she likely to absolutely kill it on the reading section (her strongest language skills are in writing, which is not assessed). So is there any reason to do this?

I would say no, unless she is wanting to take it.

DS 13 took the ACT at the end of 6th. We were in the same boat, no real reason to take it.

He is a great test taker and I wanted to see where he fell compared to other test he had taken in the past through NUMATS (NWEAs, EXPLORE....).

After the test he asked "why exactly did he take this test". I said the same reasons you took the EXPLORE in 3rd grade—just part of the bigger picture—shrug.

I am not sure it was good or bad but looking back it accomplished nothing really. He did a great job just like I thought he would.

The test dates aren't very good for us as a family, so that's also a factor. ACT dates are better than SAT. She is meh to neutral on taking it.

The main reason we did SAT/ACT at that age was for homeschool documentation, and maybe a little bit to help me in instructional planning. Didn't even register through TIP, CTY, etc., as attending programs/having certificates wasn't an interest. And we didn't bother with the test-anxious one. (Used other assessment tools, instead.)

If your DD is neutral, I would nudge her to try it. Expected and unexpected benefits may accrue. We registered through NUMATS because DS and DD were only 12 and couldn't register online otherwise. As a result, they participated in the College Board study where they got to take a second (new version) SAT for free plus received a giftcard for their participation. We subsequently registered with CTY as well for the ceremony (closer than NUMATS) and the one course scholarship donated by colleges. I was pretty sure that DS would be awarded a scholarship but was pleased that he got one from a prestigious college rather than a mediocre one. A summer college course is within our plans in a couple of years so it's nice to save a couple of thousand dollars in tuition. However, I was surprised that DD also received the same scholarship because her scores weren't even SET (700+) level. Your description of your DD fits mine as well - not a math genius and not likely to absolutely kill it on the reading section. DD's scores were only around DYS level but I think it helped that not just one but all three section scores were strong and she can obviously write based on the SAT essay. Her Reading score was the strongest of the three while her Language/Writing score was the weakest. If your DD is strongest in Language/Writing, consider registering with CTY instead because it looks like they will be using the combined reading/language (EBRW) score rather than just the reading subscore moving forward. CTY also gives a giftcard to students who qualify for the Grand Ceremony and provides a free lunch and campus tour afterwards. I don't know much about Duke TIP but NUMATS also awards top scorers although it's not advertised so I was surprised when DS received a $600 tuition scholarship useable on NUMATS courses.

In addition to the potential monetary incentives, there were a couple of other benefits that I had not considered at the time they tested. DS and DD can automatically enroll in our community college system without any placement testing. The requirement is scores no lower than 500 all three (Math, Critical Reading and Language/writing) sections. More importantly, DD in particular has been inspired to pay more attention to academics, work on her language skills, maximize her other standardized testing scores, and contemplate college and career options.

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.

My son will be taking the SAT this year in seventh grade. I think we are doing the right amount of acceleration for him. I am hoping that the data ferom this will help with scheduling for next year. And possibly we might be applying for DYS if he gets qualifying scores.

My son took it in 7th grader for fun. He loves taking standardized tests. He did really well on it and qualified for both math and verbal with Duke. They invited him to retake it 2 months later to compare his score with the old and new SAT and got basically the exact same score.
He took last summer a 5-week high school Geometry class last summer at the community college. He did really well in it and the teacher really encouraged him to skip out of Integrated Math 1 for 8th grade, which is what the accelerated 8th graders take.
Our school finally allowed him to do that, really because they were super impressed by his Duke TIP medal and math SAT scores! Although that wasn't why he took it in the first place.
He has a solid A in Integrated Math 2 as an 8th grader. He said he's very happy he skipped ahead