  Understanding the explosion mechanism and hydrodynamic evolution of
core-collapse supernovae is a long-standing quest in astronomy. The asymmetries
caused by the explosion are encoded into the line profiles which appear in the
nebular phase of the SN evolution -- with particularly clean imprints in He
star explosions. Here, we carry out nine different supernova simulations of
He-core progenitors, exploding them in 3D with parametrically varied neutrino
luminosities using the $\texttt{Prometheus-HotB}$ code, hydrodynamically
evolving the models to the homologeous phase. We then compute nebular phase
spectra with the 3D NLTE spectral synthesis code $\texttt{ExTraSS}$ (EXplosive
TRAnsient Spectral Simulator). We study how line widths and shifts depend on
progenitor mass, explosion energy, and viewing angle. We compare the predicted
line profile properties against a large set of Type Ib observations, and
discuss the degree to which current neutrino-driven explosions can match
observationally inferred asymmetries. With self-consistent 3D modelling --
circumventing the difficulties of representing $^{56}$Ni mixing and clumping
accurately in 1D models -- we find that neither low-mass He cores exploding
with high energies nor high-mass cores exploding with low energies contribute
to the Type Ib SN population. Models which have line profile widths in
agreement with this population give sufficiently large centroid shifts for
calcium emission lines. Calcium is more strongly affected by explosion
asymmetries connected to the neutron star kicks than oxygen and magnesium.
Lastly, we turn to the NIR spectra from our models to investigate the potential
of using this regime to look for the presence of He in the nebular phase.
