The members weren’t allowed to choose Badenoch, she was eliminated at an early stage by the MP vote, probably because she was too radical and lacked ministerial experience.
Rishi Sunak was claiming to be resident in the US while Chancellor of the Exchequer, while his wife was claiming non dom status to avoid paying tax. He was also hated by the supporters of the previous PM because he wielded the knife.
It’s not a shock that elections are not won on competence.