[chalst]

A university that has a reputation for doing this will attract less funding.

This isn't a new phenomenon. Most of the money that comes to successful departments comes from research funding, usually from the big funding agencies, and the risk is more that the university admin lavishes attention and resources on the most visibly successful departments, and so sacrificing breadth and the strength of their interdisciplinary work. Look at the recent Kings College London fiasco for a recent example.