In recent years, illiberal populist governments around the world have taken action against the concept of an independent judiciary. Their argument is that the courts don't reflect the will of "the people."
For the record, I don't agree with their approach, but there is a fundamental truth beneath that populist argument.
How about splitting the Supreme Court instead? One court should be the supreme court of appeals. Here, an independent judiciary is crucial, as the point of Magna Carta was to prevent the government from stacking the courts in pursuing criminal cases and typical civil cases. The other court, however, should be politically accountable: the supreme constitutional court.
Once upon a time, the early United States had a different arrangement of power than today. The original Supreme Court functioned as the supreme court of appeals. The function that evolved into judicial review once belonged to the statesmanlike presidency; Washington and his immediate successors were each a one-man judicial review show, exercising the majority of their vetoes against bills they deemed to be unconstitutional.
The fundamental truth beneath this original arrangement is that judicial review, whether a law is constitutional or not, is fundamentally legislation from the bench or judicial activism, no matter the hypocritical distinctions made by legal conservatives between their preferred legal interpretations and liberal legal interpretations.
Bolivia is a model for regular judicial elections that can be applied to the supreme constitutional court. Furthermore, judges there should be recallable.