The current process for appointing Supreme Court justices is broken, and this is largely because of how lifetime tenure has distorted and politicized the system.
Justices often try to retire during the presidency of someone sympathetic to their judicial philosophy. This doesn’t always work—Justice Ruth Bader Ginsburg died trying to wait out President Trump. But, overall, this gives the justices too much power in picking their own successors. And that ability also creates the impression that the justices are more political actors than judges, which damages the rule of law.
No other major democracy in the world gives the justices on its highest court life tenure, nor do 49 of the 50 U.S. states. The longest terms are more like the 12-year terms served by German Constitutional Court justices. Countries and states that don’t have term limits have mandatory retirement ages; many places have both.