  During the early history of unitary quantum theory the Kato's exceptional
points (EPs, a.k.a. non-Hermitian degeneracies) of Hamiltonians $H(\lambda)$
did not play any significant role, mainly due to the Stone theorem which firmly
connected the unitarity with the Hermiticity. During the recent wave of
optimism people started believing that the corridors of a unitary access to the
EPs could be opened leading, say, to a new picture of quantum phase transitions
via an {\it ad hoc} weakening of the Hermiticty (replaced by the
quasi-Hermiticity). Subsequently, the pessimism prevailed (the paths of access
appeared to be fragile). In a way restricted to the quantum physics of closed
systems a return to optimism is advocated here: the apparent fragility of the
corridors is claimed to follow from a misinterpretation of the theory in its
quasi-Hermitian formulation. Several perturbed versions of the realistic
many-body Bose-Hubbard model are chosen for illustration purposes.
