I am one of the StackOverflow "mod" in the legendary category. I am also no longer visiting StackOverflow.
There is no "mod selection process". You will gradually gain more karma when you write questions and answers and get upvotes. With more karma, you can unlock features like closing down bad questions.
I feel that a lot of the StackOverflow bad onboarding experience issues ("your question is closed down") come from the fact that StackOverflow had poor tools to support niche communities, in the case of experts and cross-cultural issues, in the case of juniors asking help. It's important to note that these are two distinct problems and the latter is a problem on a much bigger scale ("number of no-value questions and answers"). Nevertheless, both of them lead to the degeneration of usefulness of StackOverlow ("why to go there if you are not going get help.")
Both of these issues could have been addressed, though. StackOverflow tried to tackle these issues, but it was too little, too late, for example, by having "staging grounds" for new users and new questions. For expert topics, StackOverflow stopped giving enough back to the experts themselves, as in your reputation stopped having value, and there is no longer incentives just to answer the questions for the sake of helping other people. This could be simply solved by having paid answers or paid questions.