Since Minato used the Eight Trigrams Seal and the Four Elements Seal to seal Yang Kurama into Naruto, why didn't he use the same set of seals on himself to seal the Yin half? Why Reaper Death Seal? Or into Kushina? Seems like a pointless sacrifice. And waste of Yin Kurama's potential.
Naruto chapter 503, page 17:
- Minato decided to seal Kurama into Naruto, primarily because of Jiraiya's words about the "Child of Prophecy", thinking/knowing that Naruto could utilize the Tailes Beast's power to be the saviour of the ninja world.
- Minato tells Kushina that sealing the complete Kyuubi was not physically possible and they had to split the beast into the Yin and Yang halves for the sealing. Also, the entire Nine Tails' chakra was too immense to be sealed into an infant.
- Kushina was dying because of the Tailed Beast extraction and therefore she wasn't capable (or wouldn't survive) of becoming a Jinchuriki again.
Due to the aforementioned reasons, Minato decided to seal the Yang half into Naruto (so Naruto could harness the power for good) and the Yin half into himself (as sealing the entire Kurama wasn't possible).
Minato and Kushina decided that Naruto could become the said child of prophecy with the power of the Kyuubi. Since the entire Kyuubi couldn't be sealed into the infant Naruto, Minato had to use the Reaper Death Seal. So the Kurama's power could be brought down to seal him into Naruto. Also, the Reaper Death Seal allowed Minato to choose which half of Kurama should be sealed into Naruto.
So essentially, Minato did become the Yin Kurama's jinchuriki and remained that way. But the loss of using the Reaper Death Seal is that, it seals the user's life too. Minato sealed Yang Kurama into Naruto by becoming Yin Kurama's jinchuriki and at the cost of his life.