  We present an alternative protocol allowing for the preparation of critical
states that instead of suffering from the critical slowing-down benefits from
the critical speeding-up. Paradoxically, we prepare these states by going away
from the critical point which allows for the speed-up. We apply the protocol to
the paradigmatic quantum Rabi model and its classical oscillator limit as well
as the Lipkin-Meshkov-Glick model. Subsequently, we discuss the application of
the adiabatic speed-up protocol in quantum metrology and compare its
performance with critical quantum metrology. We show that critical quantum
metrology with the Lipkin-Meshkov-Glick model cannot even overcome the standard
quantum limit, and we argue that, even though critical metrology protocols can
overcome it in some cases, critical metrology is a suboptimal metrological
strategy. Finally, we conclude that systems exhibiting a phase transition are
indeed interesting from the viewpoint of quantum technologies, however, it may
not be the critical point that should attract the most attention.
