Oomis, if logic doesn’t take the place of intuition, intuition doesn’t take the place of logic, either. You can’t have it both ways.
As I pointed out, even Nevua and Ruach Hakodesh can’t Pasken.
Sarah Imeinu said that from Nevua, as Chazal tell us. Rivka Imeinu also did that from Ruach Hakodesh, as Chazal tell us. Intuition is good to say something seems amiss although you can’t put your finger on it. It does not apply to making a decision about who is fit for starting Klal Yisroel.