Halevai
“In fact, we don’t ‘Pasken‘ like any of Shlomo Hamelech’s trick Psakim. ”
A melech doesnt have to decide a case based on accepted klalei hapesak.
Similarly when Dovid was asked what he would do with someone who stole a poor mans only sheep, his reply was not. Easy he has to pay back 4 times.
(I dont have a source of this off hand, but Rabbi Reisman often mentions it when discussing why we refer to Hashem as “melech” so much yomim noraim time, he explains its becasue a melech can take extraneous things (like motherly love or the fact that it was the only sheep) while a ordinary judge can not, we are asking Hashem to have rachmanus on us that we may not deserve if strictly judged al pi din))