As one Justice leaves, they could only be replaced by someone from the vacant district.
In this theoretical model, the president still picks, but the pool is limited by circuit (and potentially culture contained in the circuit.)
My theory, the most liberal nominee from the 4th circuit is likely more conservative than the most liberal person from the 9th Circuit. Contrariwise, the most conservative person from the 9th circuit court of appeals is likely to still be more liberal than the most conservative person from the 4th circuit court of appeals.
Why
This would create a sense of whole nation legal representation. Not just a majority of talented legal minds from the DC Circuit.
The court would still contain an odd number to offset the probability of a tie vote.
The court would still trade off occasionally between being conservative/liberal controlled. Each district still contains legal minds across the political spectrum, but there is a higher likelihood of cultural differences between a Georgia Conservative and a California Conservative. There are cultural differences between a New York democrat and Louisian Democrat. This model accounts for and embraces variation.
There is also an opportunity for variation in legal expertise. Different circuits have different common case types. Some circuits you may be able to throw a rock and hit an environmental law expert, or a patent law expert, or a tribal dispute expert. This model aims to diversify the legal aptitude of the Supreme Court.
How
One president would not be able to start this plan… or it would be court packing. If this had to happen in one presidential term, the controlling wing of the courts party would suggest the balancing Justices to the president.
In illustration. Our court is now 9 Justices, with a 6 conservative to 3 liberal balance. So if adding 4 more Justices; the President would get the customary 2 picks and the conservative senators would suggest 2 picks. In theory this would create a 8 conservative to 5 liberal balance, not much different from the current. Those circuits not represented would need to be added in the new picks. As justices leave the court those unrepresented districts would be picked from, starting chronologically, until all districts have the required justice.
If this were to happen over multiple presidential terms, then each elected president would get 1 pick until the court is at 13. One pick from a non-represented circuit. If a vacancy also comes up, then a pick from a non-represented circuit until all are represented.
Once all circuits are represented by 13 Justices the normal process of appointing will resume, so long as each Justice is only replaced by another legal mind from the same circuit.
BUT … a dream is a wish your heart makes.
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UNITED STATES COURTS, Court Role and Structure, (April 21, 2022) https://www.uscourts.gov/about-federal-courts/court-role-and-structure.
