If they are good, I would submit them. My DD submitted hers and received 3 different ROTC scholarships. If you have have good SAT IIs, you may also want to submit those since the top schools will want them as well.
My belief is that if you have great scores, it will not hurt you to submit them.
True it would look good only if you have 5s and 750+ on your SAT Subject Tests. If anything lower I don’t think it would impress them because they don’t require it. They cannot even give you extra academic points because they don't evaluate it against other candidates.
I would think of the cost. Not knowing we sent ours in and the cost exceeded $1,000 just on test scores. If we had to do it over, I would only send 2 best tests. If you have to take many, wait until you have taken and exhausted your performance. Then choose your best 2 or 3. Sharing 2 tests is better than 3.
I would send only what schools require and suggest to take and that’s SAT or ACT for SAs. I would only send your better test/s. Also don't get excessive or obsessed with super scoring. Send only your few best scores and not all scores. If you took 10 ACTs, send in only your best 2, maybe 3. To Navy and NROTC only 2 since they only evaluate English and Math. Test scores cost $10-$15 per test sent to each schools.
For other top schools, I would only send if they suggest Subject tests. 5 on AP does not replace B on the course nor 5 on AP replaces poor SAT Subject Test if required or suggested.
Your AP grade on transcript is what really matters, because it counts towards your Weighted GPA. Not the AP Test Score. You only need to send in AP Scores to one college you will matriculate if you want to place out of some classes with 4/5 scores. We didn’t send any AP scores and DS did just fine.
Think of time and money. The cost can easily run up $2-3,000 to your parents.