Unbeknownst to many, the Shinigami of the Reaper Death Seal is a woman:
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The Reaper is a Hannya Demoness who are all females and solely females.
The Shinigami is also a priestess holding a prayer beads and reciting a prayer before commencing the sealing ritual:
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The Reaper's initial stance with it arms spread is a clerical/priestly stance:
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Like Rikūdou/Hagoromo's stance:
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It was established and well known by now that the Shiki Fūjin required Rikūdo/Hagoromo's Tablet as the catalyst for the Shinigami Mask to unseal the Reaper:
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It is because the Shiki Fūjin is Rikūdo/Hagoromo's Jutsu
and the Reaper is most probably Kaguya Ōtsutsuki, Rikūdo/Hagoromo's mother:
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As to why Kaguya became the Shinigami of the Shiki Fūjin, Kishimoto has not yet explained or revealed why, either as an end effect of eating the Shinju's fruit or as a mother's sacrifice to aid her son in fighting the Jūbi.