To investigate the potential abundance and impact of nuclear black holes (BHs) during reionization, we generate a neural network that estimates their masses and accretion rates by training it on 23 properties of galaxies harbouring them at $z=6$ in the cosmological hydrodynamical simulation Massive-Black II. We then populate all galaxies in the simulation from $z=18$ to $z=5$ with BHs from this network. As the network allows to robustly extrapolate to BH masses below those of the BH seeds, we predict a population of faint BHs with a turnover-free luminosity function, while retaining the bright (and observed) BHs, and together they predict a Universe in which intergalactic hydrogen is $15%$ ionized at $z=6$ for a clumping factor of 5. Faint BHs may play a stronger role in H reionization without violating any observational constraints. This is expected to have an impact also on pre-heating and -ionization, which is relevant to observations of the 21 cm line from neutral H. We also find that BHs grow more efficiently at higher $z$, but mainly follow a redshift-independent galaxy-BH relation. We provide a power law parametrisation of the hydrogen ionizing emissivity of BHs.