I think the permutation is because it works better on a comedic level. Probably started out as basic “But what if king Solomon did cut the baby in half” arguments and eventually became a general joke. The base level of “cut the baby in half” is already dark by itself all it takes is going through with it and you have a good bit of dark humor.

Also the whole scenario of king Solomon almost comes across as him not necessarily being particularly smart but moreso that the people he was dealing with were crazy or stupid.