To determine whether requiring the test “adds something” besides being a duplicate confirmation, you need to compare the result with the test added to the application and without the test added to the application. This is different from looking at whether the test is correlated with something in isolation, without considering the rest of the application.
For example, some colleges support an optional 3rd LOR. How would you determine whether that optional 3rd LOR “adds something” and should be required? If you reviewed whether the 3rd LOR is correlated with outcome in isolation, you’d probably find that the 3rd LOR has a statistically significant correlation without outcome, so you might conclude a 3rd LOR should be required. Using the same logic, you might conclude a 4th, 5th, and 6th LOR should also be required since each LOR has a statistically significant correlation without outcome in isolation, without considering anything else in the application. However, if you looked at whether the 3rd LOR adds something beyond the other 2 LORs and rest of application; I expect you’d come to a very different conclusion about how much the 3rd LOR adds to predicting outcome, and instead would be fine with the 3rd LOR remaining optional.