  In a series of papers, we have recently demonstrated that it is possible to
construct stellar structure models that robustly mimic the stratification of
multi-dimensional radiative magneto-hydrodynamic simulations at every time-step
of the computed evolution. The resulting models offer a more realistic
depiction of the near-surface layers of stars with convective envelopes than
parameterizations, such as mixing length theory, do. In this paper, we explore
how this model improvement impacts on seismic and non-seismic properties of
stellar models across the Hertzsprung-Russell diagram. We show that the
improved description of the outer boundary layers alters the predicted global
stellar properties at different evolutionary stages. In a hare and hound
exercise, we show that this plays a key role for asteroseismic analyses, as it,
for instance, often shifts the inferred stellar age estimates by more than 10
per cent. Improper boundary conditions may thus introduce systematic errors
that exceed the required accuracy of the PLATO space mission. Moreover, we
discuss different approximations for how to compute stellar oscillation
frequencies. We demonstrate that the so-called gas $\Gamma_1$ approximation
performs reasonably well for all main-sequence stars. Using a Monte Carlo
approach, we show that the model frequencies of our hybrid solar models are
consistent with observations within the uncertainties of the global solar
parameters when using the so-called reduced $\Gamma_1$ approximation.
