  We address the question of the role of low-energy nuclear physics data in
constraining neutron star global properties, e.g., masses, radii, angular
momentum, and tidal deformability, in the absence of a phase transition in
dense matter. To do so, we assess the capacity of 415 relativistic mean field
and non-relativistic Skyrme-type interactions to reproduce the ground state
binding energies, the charge radii and the giant monopole resonances of a set
of spherical nuclei. The interactions are classified according to their ability
to describe these characteristics and we show that a tight correlation between
the symmetry energy and its slope is obtained providing $N=Z$ and $N\ne Z$
nuclei are described with the same accuracy (mainly driven by the charge radius
data). By additionally imposing the constraints from isobaric analog states and
neutron skin radius in $^{208}$Pb, we obtain the following estimates:
$E_{sym,2}=31.8\pm 0.7$ MeV and $L_{sym,2}=58.1\pm 9.0$ MeV. We then analyze
predictions of neutron star properties and we find that the 1.4$M_\odot$
neutron star (NS) radius lies between 12 and 14 km for the "better" nuclear
interactions. We show that i) the better reproduction of low-energy nuclear
physics data by the nuclear models only weakly impacts the global properties of
canonical mass neutron stars and ii) the experimental constraint on the
symmetry energy is the most effective one for reducing the uncertainties in NS
matter. However, since the density region where constraints are required are
well above densities in finite nuclei, the largest uncertainty originates from
the density dependence of the EDF, which remains largely unknown.
