I think this is exactly right. My S24 really isn’t sure what he wants to study, but some engineering disciplines are on the list. But the list also contains subjects like cognitive science, linguistics, political science, and economics. He also really loves his literature and history classes, even though he doesn’t think he would major in any of those. He probably is not a candidate for a “top 20” school, but we have found those seem to be the schools that offer the most flexibility for exploring a variety of majors across multiple disciplines that include engineering, and then choosing what you want to do without much hassle.
Except for a handful of schools, if he wants to consider engineering outside those “top” schools, his only feasible option is to apply as an engineering major, and then transfer from the engineering school to the school of arts & sciences if he decides it’s not what he wants, since transferring in to the engineering school is often impossible or nearly so.
Given that the type of job that (today 
) is most intriguing to him is some type of consulting, that makes the elite schools even more attractive. Since that is our experience, I can imagine that there are many people in a similar situation. I think students who are like him – good at math and science, but also interested in a wide variety of more liberal arts type subjects – are more likely to be drawn to careers that are not strictly engineering jobs, even if they enjoy and a major in Engineering in college.