  The diffuse cosmic supernova neutrino background (DSNB) is observational
target of the gadolinium-loaded Super-Kamiokande (SK) detector and the
forthcoming JUNO and Hyper-Kamiokande detectors. Current predictions are
hampered by our still incomplete understanding of the supernova (SN) explosion
mechanism and of the neutron star (NS) equation of state and maximum mass. In
our comprehensive study we revisit this problem on grounds of the landscapes of
successful and failed SN explosions obtained by Sukhbold et al. and Ertl et al.
with parametrized one-dimensional neutrino engines for large sets of
single-star and helium-star progenitors, with the latter serving as proxy of
binary evolution effects. Besides considering engines of different strengths,
leading to different fractions of failed SNe with black-hole (BH) formation, we
also vary the NS mass limit, the spectral shape of the neutrino emission, and
include contributions from poorly understood alternative NS-formation channels
such as accretion-induced or merger-induced collapse events. Since the neutrino
signals of our large model sets are approximate, we calibrate the associated
degrees of freedom by using state-of-the-art simulations of proto-neutron star
cooling. Our predictions are higher than other recent ones because of a large
fraction of failed SNe with long delay to BH formation. Our best-guess model
predicts a DSNB electron-antineutrino-flux of 28.8^{+24.6}_{-10.9}
cm^{-2}s^{-1} with 6.0^{+5.1}_{-2.1} cm^{-2}s^{-1} in the favorable measurement
interval of [10,30] MeV, and 1.3^{+1.1}_{-0.4} cm^{-2}s^{-1} with
electron-antineutrino energies > 17.3 MeV, which is roughly a factor of two
below the current SK limit. The uncertainty range is dominated by the still
insufficiently constrained cosmic rate of stellar core-collapse events.
