  Non-analyticities in the logarithm of the Loschmidt echo, known as dynamical
quantum phase transitions [DQPTs], are a recently introduced attempt to
classify the myriad of possible phenomena which can occur in far from
equilibrium closed quantum systems. In this work, we analytically investigate
the Loschmidt echo in nonequilibrium $s$-wave and topological $p_x+ip_y$
fermionic superfluids. We find that the presence of non-analyticities in the
echo is not invariant under global rotations of the superfluid phase. We remedy
this deficiency by introducing a more general notion of a grand canonical
Loschmidt echo. Overall, our study shows that DQPTs are not a good indicator
for the long time dynamics of an interacting system. In particular, there are
no DQPTs to tell apart distinct dynamical phases of quenched BCS
superconductors. Nevertheless, they can signal a quench induced change in the
topology and also keep track of solitons emerging from unstable stationary
states of a BCS superconductor.
