An argument for Supreme Court term limits:
For starters, because judges have lifelong terms, openings on the court come at totally random intervals. As a result, the number of judges any given president appoints varies widely. Jimmy Carter appointed zero judges in his one term, while Bush Sr. appointed two. Clinton appointed two judges in his two terms, while Eisenhower appointed five.A fair court should, by definition, be truly impartial and balanced, especially when it represents the law of the land...
Filling up the court in such a random manner makes its overall political composition more random as well, rather than a democratic reflection of the political trends of the country as a whole.
Indeed, it is worse than mere randomness. Supreme Court judges are not replaced only when they die, but also when they retire. This makes it possible for judges to strategically retire only when they are certain they will be replaced by a president with the same ideological commitments.