For a gas in a mass-sealed container, average vx, vy, vz are also zero, just as in the shaft, so this trivially matches.

You're correct that I should have said speeds, and I should have mentioned that the shaft requires a special shape/density distribution, but the point stands: The molecular property distribution doesn't by itself tell you how cold something is, or how much energy can be extracted -- it's also relevant how its degrees of freedom are constrained, which shows how your knowledge of (mutual information with) the system matters.