Most of the Ivy League business schools are graduate only. For example, you can’t major in business as an undergrad at Columbia, Harvard, Dartmouth, Princeton, Cornell, or Yale (although there is a special undergraduate concentration in business you can do at Columbia - it’s like a minor - but it’s by application only and slots are limited). You can major in commerce, organizations, and entrepreneurship at Brown, and of course Penn has the Wharton school.
Here’s the thing - ‘business’ is a catch-all term. There are lots of things that are ‘business.’ Do you want to simply work at a business, or do you want to go into fields that are commonly defined as business like marketing, finance, or accounting? You can do marketing, finance, or management with majors in other areas; you don’t have to study them in undergrad at all.
If you want to be an engineer or a software developer, then yes, you should gain technical skills and major in engineering or computer science. If you want to manage people in those roles, then you probably should also get a technical degree. You can also take on roles that have a little bit of a hybrid, like operations research or program management, if you have a technical degree. Many students with quantitative majors like math, statistics, physics, and economics go onto manage hedge funds and do investment banking and all that.