This is a detailed study comprising scability concern about Ram-air wings. Page 532: " A prime example of the scaling process is documented nicely in the X-Fly family
of Ram-air precision cargo delivery systems from Airborne Systems North America
[9, 11]. The development originated as an Advanced Concept Technology Demonstrator
research program from Natick Soldier Systems, whereby iteratively heavier
weight requirements were levied (0.25 ton, 1 ton, 2.25 tons, 4.5 tons, 13.5 tons, and
finally 19 tons). The wing sizes were 36 m2, 102 m2, 250 m2, 350 m2, 900 m2,
and 1,040 m2, respectively."
So scaling the flexible kite leads to a mass penalty, although far lesser than for the rigid kite.
Apart from this paper, it looks that the power kite can deliver high power by translation like for kite ship, while the rigid wing would be suitable for energy production, but there is no still definitive answer.