  Phase transitions in the early universe lead to a reduction in the equation
of state of the primordial plasma. This exponentially enhances the formation
rate of primordial black holes. However, this sensitivity to the equation of
state is the same that primordial black hole abundances show to the primordial
curvature power spectrum amplitude. In this paper, we investigate peaked power
spectra and show the challenges associated with motivating populations of
primordial black holes with standard model enhancements. The parametrisation of
different power spectra plays an important role in this discussion. The allowed
parameter space consistent with a large QCD phase transition impact on the
primordial black hole abundance differs greatly. This is particularly evident
for wider spectra.
