Elizabeth Warren got her undergraduate degree from University of Houston and her law degree at Rutgers. That didn’t stop her from later on teaching at Harvard Law. Mike Pence attended Indiana University and McKinney school at law. That didn’t stop him from being a congressman, governor or Vice President. The idea that “power” can only originate from an Ivy League school ignores so many examples of powerful people who never attended one.
Furthermore, an undergraduate from a lesser known school won’t prevent entry to an Ivy if that is the goal. I know a senior from one of those “mediocre” schools who give merit aid who has been accepted to Harvard Law. A classmate is heading off to Stanford (not that it’s an Ivy…) And even Clarence Thomas started at College of the Holy Cross before heading off to Yale for law school.
(Sorry that all my examples are politicians. I was a policy sci major 
)
There’s nothing wrong with Ivies (especially if you can afford them) but not attending one is certainly not the end of the world no matter what your long term goal is.