FWIW since you are asking the question:
This came up recently with a friend, for SAT:
Common app for many schools has “self report” the verbal and math for the highest verbal score sitting , and then asks for the verbal and math for the date with highst math. I have seen this for many schools for SAT.
The kid had 710 & 650 on one test, 700 and 700 on the other. The advice of the counselor was to just report the 700-700, to those schools where all four numbers would need to be reported, because the benefit of the 10 points did not outweigh “seeing” the 650. Parent asked my opinion and i said go w what the counselor said to do. This kid wants Stem and the 650 is a math score.
So. The schools do say they superscore and i agree you can’t spend time worrying BUT there are well-regarded counselors out there who in certain situations think it may make sense to just report the single score.