If Elena Kagan worked a "Miracle at Harvard," what effect might she have on the Supreme Court?

An essay by University of New Mexico lawprof Kevin K. Washburn:

For most of the past fifty years, attending Harvard Law School was a miserable experience....

During Elena Kagan’s tenure as dean, a miracle occurred. Harvard Law School was transformed. Today, students embrace the institution. The professors engage with one another. And the school’s widely discussed dysfunctions are distant memories. Kagan accomplished this miracle by modeling two important and traditional American values: hard work and community. Kagan was known for walking the halls tirelessly to learn the views of her bright and independent colleagues and to seek consensus. She broke the gridlock between faculty political factions that had atrophied the academic life of the institution. Even more importantly, she transformed the student experience. This essay seeks to describe Kagan’s transformational leadership and provide insight as to the specific changes Kagan made to accomplish the miracle.

Let's take this all as true. Kagan has skills that worked brilliantly in the context a dean transforming a deeply dysfunctional, highly elite law school. But how will those skills apply in the context of an individual Justice on the Supreme Court? When a troubled law school brings in a new dean, it is looking for leadership and transformation. But there is no reason to think that the Supreme Court Justices look toward the newcomer for leadership at all, and she arrives to fill the seat that was vacated, not with any problem to be solved and institution to be transformed.