That's a really neat problem, Carl; I've never seen it before.
I do think I have the answer, however. The stated claim appears
to be correct for the hypothetically ideal problem posed. The
"reason" that you can compress the gas arbitrarily far by
dribbling weight onto the piston is that in that case you would
do *less work* on the gas than was done by dropping the weight
from the initial height, and as a result the gas is not raised to
as high an internal energy.
Higher compression results when you compress the gas more gently!
I will note that the equilibration process itself is implicitly
irreversible. The process itself may be adiabatic*, but if it is,
then irreversible work is done on the gas. This can occur because
pressure gradients are set up in the gas, and their relaxation
may lead to the hypothetically prescribed end state, though that
would probably not be the correct mechanism for a real system.
Leigh
*Here is a case where it makes no difference what you call the
process, but just using the word "adiabatic" can be misleading.
For instance, the adiabatic gas law clearly cannot be applied to
the solution of this problem. "Adiabatic" merely means that
there is no heat from outside the system.