The neutrino-driven wind, which occurs after the onset of a core-collapse supernova explosion, has long been considered as the possible site for the synthesis of heavy $r$-process elements in the Universe. Only recently, it has been possible to simulate supernova explosions up to $\sim 10\mathrm{seconds}$, based on three-flavor Boltzmann neutrino transport. These simulations show that the neutrino luminosities and spectra of all flavors are very similar and their difference even decreases during the deleptonization of the proto-neutron star. As a consequence, the ejecta are always proton rich which rules out the possible production of heavy $r$-process elements ($Z>56$). We perform a detailed analysis of the different weak processes that determine the neutrino spectra. Nonelectron flavor (anti)neutrinos are produced and interact only via neutral-current processes, while electron (anti)neutrinos have additional contributions from charge-current processes. The latter are dominated by ${\nu }_e$-absorption on neutrons and ${\overline{\nu }}_e$-absorption on protons. At early times, charge-current processes are responsible for spectral differences between ${\nu }_e$, ${\overline{\nu }}_e$ and ${\nu }_{\mu /\tau }$. However, as the region of neutrino decoupling moves to higher densities during deleptonization, charge-current reactions are suppressed by final state Pauli blocking. ${\overline{\nu }}_e$ absorption on protons is suppressed due to the continuously increasing chemical potential of the neutrons. ${\nu }_e$ absorption on neutrons is blocked by the increasing degeneracy of the electrons. These effects result in negligible contributions from charge-current reactions on time scales on the order of tens of seconds, depending on the progenitor star. Hence, the neutrino spectra are mainly determined from neutral-current processes which do not distinguish between the different flavors and result in the convergence of the spectra. These findings are independent of the charge-current reaction rates used. It rules out the possibility of neutron-rich ejecta at late times and the production of heavy $r$-process elements from nonrotating and not magnetized proto-neutron stars.

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