  Many late time approaches for the solution of the Hubble tension use late
time smooth deformations of the Hubble expansion rate $H(z)$ of the
Planck18/$\Lambda$CDM best fit to match the locally measured value of $H_0$
while effectively keeping the comoving distance to the last scattering surface
and $\Omega_{0m} h^2$ fixed to maintain consistency with Planck CMB
measurements. A well known problem of these approaches is that they worsen the
fit to low $z$ distance probes. Here we show that another problem of these
approaches is that they worsen the level of the $\Omega_{0m}-\sigma_8$ growth
tension. We use the generic class of CPL parametrizations corresponding to
evolving dark energy equation of state parameter $w(z)=w_0+w_1\frac{z}{1+z}$
with local measurements $H_0$ prior and identify the pairs $(w_0, w_1)$ that
satisfy this condition. This is a generic class of smooth deformations of
$H(z)$ that are designed to address the Hubble tension. We show that for these
models the growth tension between dynamical probe data and CMB constraints is
worse than the corresponding tension of the standard Planck18/$\Lambda$CDM
model. We justify this feature using a full numerical solution of the growth
equation and fit to the data, as well as by using an approximate analytic
approach. The problem does not affect recent proposed solutions of the Hubble
crisis involving a SnIa intrinsic luminosity transition at $z_t\simeq 0.01$.
