I do not think everyone who wants to go to an Ivy league school is simply chasing status. I went to Harvard for medical school because I felt, frankly, it was the best in the USA. I found most of the lecturers to be phenomenal, the physical structure of the place (the library, the computers), to be incredible, the resources were spectacular.
My classmates were similarly incredible.
Having some very elite names on my resume has helped me long-term pursue my dreams/goals, which were not to work at elite companies. It has opened lots and lots of doors. We hope our children will also go to Ivy league (or similar) schools since it opens lots of job opportunities and affords unique life/learning experiences.