A budding musician once came up to me and ask my advice if she should go to Berklee College of Music. I asked her why she wanted to go. She said that she wanted to become a working Pop singer and a producer. I asked her if she knew how much Berklee cost at that time? At the time, it cost somewhere around $16,000 a semester. To do the basic math: it would have cost her around $128,000 (USD) in total to get a degree from Berklee and that was just to cover tuition. That didn't even cover rent or food or basic living costs. I then said that she could take that money, invest in buying some great music gear, and then go intern in a working studio for free. That way, she'd get the education she wanted and then also have connections from the producer she was working with. In the end she opted for getting the "prestige" of Berklee and only ended up lasting a semester.
The thing about Ivy League is the allure it has to having "prestige" associated with your name. The problem with prestige is that it needs to match the environment it's going into or ultimately it doesn't work.
For example, I work in a musical environment. Saying that I graduated from Berklee has never gotten me a single gig. But if I said that I had played backup for David Bowie or Dave Matthews then suddenly my "prestige" can work in the environment I work in.
If a doctor graduates from Oxford or Harvard then her "prestige" matches the environment she's going to be working in. If, however, she's best buds with Will Smith or Taylor Swift then that doesn't make for a "leg-up" in moving forward in her career.
Prestige can work. But it must match the environment that can help it flourish in.
Consider what environment you're moving into before spending hundreds of thousands of dollars you may not pay off until your mid-40s.