King Solomon

I don’t know if the midrash are trying to reconstruct history as it was. A midrash can also be written for educational purposes. In general, even in halacha, the sermon is not bound by the rules of the Peshat. The verses are written in a way that can be interpreted both through the sermon and through the Peshat, so that we may learn from them the messages that emerge from both readings. It is indeed difficult to accept that a legendary sermon that deals with facts (what happened to Solomon) simply ignores the facts completely. Perhaps a sermon can be seen as a kind of caricature. The caricature sometimes greatly magnifies one aspect (a funny mole or deformity that a person has) and ignores all the other aspects. Therefore, it is possible that Solomon also had such an aspect, but within the framework of the whole, it is only one aspect. The simple description describes the whole and the sermon focuses on this aspect, which indeed existed but was marginal or partial. For example, anyone who says David sinned is simply mistaken. I assume that it is clear to the Sages that he sinned. They wanted to focus on the formal halakhic aspect that he did not sin against anyone’s wife (because anyone who goes to war against the House of David gives his wife a conditional divorce). But the moral sin certainly was. Rabbi Yaakov Midan emphasized this in his book on the sin of David and Bathsheba. You are focusing on one aspect that does not describe the whole, but in itself is correct.