  We show that the quantum Fisher information attained in an adiabatic approach
to critical quantum metrology cannot reach the Heisenberg limit of precision
and therefore \emph{regular} quantum metrology under optimal settings is always
superior. Furthermore, we argue that even though shortcuts to adiabaticity can
arbitrarily decrease the time of preparing critical ground states, they cannot
be used to achieve or overcome the Heisenberg limit for quantum parameter
estimation in adiabatic critical quantum metrology. As case studies, we explore
the application of counter-diabatic driving to the Landau-Zener model and the
quantum Rabi model.
