Kinetic backreaction cannot suppress axion quantum pressure

Ultralight axions from string compactifications carry non-canonical kinetic terms whose normalization is set by a coupling function that depends on an accompanying modulus field. As dark matter, such an axion forms a cold condensate whose quantum pressure resists gravitational collapse below a Jeans scale fixed by that coupling. One might hope that backreaction from the condensate's oscillations could shrink this Jeans length and thereby enhance structure growth. We show that it cannot. For any smooth, positive coupling function, the oscillation-averaged backreaction always drives the coupling to larger values, strengthening the quantum pressure and growing the Jeans length with time. We establish this no-go result analytically through an adiabatic- invariant analysis and confirm it by direct numerical integration. Kinetically coupled dark matter therefore cannot self-generate the conditions for enhanced gravitational collapse or the seeding of structure on sub-Jeans scales.