Yet the supreme court appointees get to choose when they retire and thus they insert their own politics into who picks their own replacement. This in turn causes the supreme court appointees to rarely choose to retire when they think their retirement may switch the balance of the court in a way they find personally unsatisfying.

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What I am saying politics is built into the Supreme Court by both textual design but also by the norms of what we as a society decide is legitimate and what is illegitimate. Our language when we call the Supreme Court "a-political" is not a truthful representation of reality. Our language when we call the Supreme Court apolitical is actually the politics of the Supreme Court. This is because our language calling the court apolitical does not describe the actual reality but instead one step removed from the reality, aka what we feel comfortable with and what we see as "the norms" / "baseline."

Put another way water has a color, but when you are a fish swimming in the water you do not see the color you only see the dirt suspended in the water, you forget that water itself has a color for you are so hyperfocused on the dirt in the water you do not notice the water itself, you are so hyperfocused on the noise you do not see the baseline. The fish only sees the dirt, the other fish and the sharks and so on.