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Constraining the primary growth channel of supermassive black holes (SMBHs) 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 cosmic growth of SMBHs. 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. Indoing so, we characterize outstanding limitations associated with the existing measurements and discuss the landscape of future observational campaigns which could be planned and executed with future X-ray observatories. We focus our attention on the High-Energy X-ray Probe (HEX-P), a proposed probe-class mission designed to serve the high-energy community in the 2030s.