I can understand why we want a short connection between the station
ground (the bonded chassis) and earth ground in the case of an RF
ground, especially for unbalanced antennas. But for a lightning
ground, I am not sure I understand why we want a short connection
between station ground and earth.

Let's take the example of an operator with whose only choice is a
second story ham shack and an antenna mounted on a pole some distance
from the house. If a balanced antenna system is used (so we don't need
a good RF ground) and the coax has an arrestor placed at the service
entrance ground where the shield is connected (cold water pipe in
basement), why do we need a ground wire at all? (The coax would run
from the antenna to the basement level [where grounded] and then up to
the second floor.) The chassis' can be bonded together and the bond
point can be connected to earth ground through the coax shield. The
lightning is not going to travel up to the second floor to get the
radio when it has a low impedance path right at ground, is it?

-JJ