Peter brings up an interseting observation about Rook values approximating
empty board mobility. Yet the short rooks seem a little weak by this
standard, just as the usual crowded board mobility makes long Rooks too
weak.
The Rook's special advantages over the Bishop and Knight (interdiction,
can-mate) are endgame advantages--so empty board mobility or at least a
higher than normal magic number might be the way to quantify the value of
different length Rooks among themselves. An R7 is much superior to an R3
in both can-mate and interdiction. And Rook disadvantages (lack of
forwardness, hard to develop) apply regardless of length so they would
cancel out in this comparison.