Industrial production of alkali metals
One aspect to consider is that the boiling points of alkali metals go down as they get heavier.
From The Encyclopedia Britannica:
Lithium:  bp = 1342°C
Sodium:  883°C
Potassium:  759°C
Rubidium:  688°C
Cesium:  671°C
Francium:  677°C (probably this one is merely predicted)
Thus the heavier alkali metals could be volatile enough to effectively escape as vapors while sodium and the chloride salts remain largely liquid.  Thereby the equilibrium that would otherwise limit the displacement of the heavier metal is pulled forward in favor of that metal being lost to the gas phase.  The vapor would later be condensed to get the metal as a solid.