  Constraining the primary growth channel of supermassive black holes (SMBH)
remains one the most actively debated questions in the context of cosmological
structure formation. Owing to the expected connection between SMBH spin
parameter evolution and the accretion and merger history of individual black
holes, population spin measurements offer a rare observational window into the
SMBH cosmic growth. As of today, the most common method for estimating SMBH
spin relies on modeling the relativistically broaden atomic profiles in the
reflection spectrum observed in X-rays. In this paper, we study the
observational requirements needed to confidently distinguish between the
primary SMBH growth channels, based on their distinct spin-mass distributions
predicted by the Horizon-AGN cosmological simulation. In doing so, we
characterize outstanding limitations associated with the existing measurements
and discuss the landscape of future observational campaigns, which can be
planned and executed with future X-ray observatories. We focus our attention on
the High-Energy X-ray Probe (HEX-P), a concept probe-class mission aimed to
serve the high-energy community in the 2030s.
