So what happens when the judges chosen for a case interpretation end up being 7-2 in one party’s favor? Conservatives would be sitting at the slot machines in a diaper pulling the lever until they hit a jackpot. It’s not like making them sit out of some cases based on a lottery is going to make them any less hypocritical or prone to power tripping and bribery. They’ll just wait their turn.
Appointees should just be subject to term limits and yearly affirmation votes by members of the BAR association to renew or revoke their qualifications. That way members of the public that are still well versed in law are able to hold them accountable.