  We explore the constraints and phenomenology of possibly the simplest
scenario that could account at the same time for the active neutrino masses and
the dark matter in the Universe within a gauged $U(1)_{B-L}$ symmetry, namely
right-handed neutrino dark matter. We find that null searches from lepton and
hadron colliders require dark matter with a mass below 900 GeV to annihilate
through a resonance. Additionally, the very strong constraints from high-energy
dilepton searches fully exclude the model for $ 150 \, \text{GeV} < m_{Z'} < 3
\, \text{TeV}$. We further explore the phenomenology in the high mass region
(i.e. masses $\gtrsim \mathcal{O}(1) \, \text{TeV}$) and highlight theoretical
arguments, related to the appearance of a Landau pole or an instability of the
scalar potential, disfavoring large portions of this parameter space.
Collectively, these considerations illustrate that a minimal extension of the
Standard Model via a local $U(1)_{B-L}$ symmetry with a viable thermal dark
matter candidate is difficult to achieve without fine-tuning. We conclude by
discussing possible extensions of the model that relieve tension with collider
constraints by reducing the gauge coupling required to produce the correct
relic abundance.
