Rigid kites scale in a similar way as wind turbine blades, undergoing almost cubed mass penalty as Dave Santos already pointed that.
Concerning flexible kites, the mass penalty is lesser but not zero. And the flight stresses add constraints making them still less durable. If we have to replace a kite (with tethers) once a year in full operation, we can see that in the end more material will be required. And plastic materials are not indefinitely recyclable, especially if they are composite, unlike aluminum for example (Recyclable Our kites are mostly made of aluminum which can easily be recycled, much better than carbon or glass fiber reinforced plastics, the material conventional wind turbines are mostly made of. Leaving no burden for the future.).
Page 532: “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.”