  The canonical scalar-tensor theory model which exhibits spontaneous
scalarization in the strong-gravity regime of neutron stars has long been known
to predict a cosmological evolution for the scalar field which generically
results in severe violations of present-day Solar System constraints on
deviations from general relativity. We study if this tension can be alleviated
by generalizing this model to include a disformal coupling between the scalar
field $\varphi$ and matter, where the Jordan frame metric ${\tilde g}_{\mu\nu}$
is related to the Einstein frame one $g_{\mu\nu}$ by ${\tilde
g}_{\mu\nu}=A(\varphi)^2 (g_{\mu\nu}+\Lambda\, \partial_\mu \varphi \,
\partial_\nu\varphi)$. We find that this broader theory admits a late-time
attractor mechanism towards general relativity. However, the existence of this
attractor requires a value of disformal scale of the order $\Lambda\gtrsim
H_0^{-2}$, where $H_0$ is the Hubble parameter of today, which is much larger
than the scale relevant for spontaneous scalarization of neutron stars $\Lambda
\sim R_s^{2}$ with $R_s (\sim 10^{-22} H_0^{-1})$ being the typical radius of
these stars. The large values of $\Lambda$ necessary for the attractor
mechanism (i) suppress spontaneous scalarization altogether inside neutron
stars and (ii) induce ghost instabilities on scalar field fluctuations, thus
preventing a resolution of the tension. We argue that the problem arises
because our disformal coupling involves a dimensionful parameter.
