Well, every kid is different. But FWIW, here’s how things played out for mine, in circumstances similar to yours (i.e., not millionaires but certainly privileged): three kids, three for three getting into their first choice (extremely selective) schools. None of the three did any summer internships or study/program during h.s. summers, though one did CTY camps until aging out. One was a three-sport athlete who did sports camps during the summer, but also had a job - literally scooping ice cream. The other two did camp-counselor type jobs over the summers. H and I feel, much as you said, that holding down a real job is an essential life skill and that h.s. is the time to start.