The issue is that the more prestigious schools, on average, tend to have have better professors which affect your LSAT scores and, to a lesser degree, more resources to help you with your extracurriculars. That said, even citing PoetsandQuants, strong extracurriculars do not replace a good GPA and test score and a deficiency in either will land an application into the waste bin fairly quickly. Looking at law school admissions profiles will show you that while most are from top universities, there is also a significant amount of admits are from less prestigious universities.
For example, this year’s Harvard Law School admits include grads from Weber State, Portland State, and UCR.
See: http://www.law.harvard.edu/prospective/jd/apply/undergrads.html
This year’s Northwestern admits include grads from CSULB, CSUN, CSUS, San Diego State, and even UC Merced.
See: https://www.law.northwestern.edu/admissions/profile/documents/undergraduate-institution-list.pdf