Nope.
The Golden Rule suffices. It cannot be reduced further.
If another was needed, that would supersede the Golden Rule.
Main point: No "side-features" that need to be ignored so as to use, a-la 1 Samuel 15:3
>>>The Golden Rule suffices
So if the question is:
Why is the golden rule morally right, the answer is: It just is.
No reason required.