1. This is a political problem, first and foremost.
2. How much it costs depends on what the school does with its network. If it offers cloud storage as part of the tuition (to offset the cost of not having much storage on the little mice) and gives the more computationally-intensive majors access to a compute cluster for the price of tuition (same reason), it could be a nice little setup.
Students would always have most of their files on them all the time, the school could buy more keyboard-laptop pairs than it buys actual computers to reduce the pressure on the public labs, and the mice could be fairly cheap if bought in bulk and resold. (OK, I know, but in theory.)
I mean, all of those arguments can be argued against, but it isn't hard to see some potential up-sides here.