As others have posted, it all depends on the school. This can change as well. UW-Madison seems to now want students to have a major in mind even though students are admitted to the university as a whole and can change majors once there. I think their current thinking is to have students motivated to plan for their future even plans alter once the college experience happens.
Your D will serve herself best if she chooses a field she likes, not one she (or your H) thinks will improve her chances of admission. Her choices of colleges will reflect her interests and available majors/classes in those. Whatever she does she should NOT try to game the system. The best schools for her will admit her because they offer her what she wants. Being at an elite school that does not give her the best opportunities in her chosen field is not the best choice for her.
She needs to look at opportunities in both economics and whichever STEM field(s) she most likes. Chemistry, math, computer science, physics, various biological majors and engineering majors are all separate fields. The best school in one may not be the best choice for a different major.
I doubt she likes all STEM fields equally. I didn’t- like chemistry, not physics… Various biology majors appeal to many premeds and seem a dime a dozen to me (I was a chemistry major and became a physician- know a math major who became a physician- both of us women back in the days of few but increasing numbers of women MD’s).
SHE needs to figure out more specific interests and plan colleges in view of potential goals. Her interests could be best served by a public flagship instead of an LAC depending on her major.
btw- despite what the “rules” are, the major needs to be chosen (and the criteria met) by the time one graduates (again, depends on the school) so it can be on the diploma…