Lexicus
Deity
In my opinion, for checks and balances between branches to work, they would need to be composed by people who are more loyal to the institution than they are to their politics.
Elite consensus, or at least a certain kind of elite consensus, is exactly the condition for this. That is "politics" as it worked in the Roman Republic, with no coherent ideological factions but ever-shifting alliances among a relatively small number of elite families who are all interrelated by marriage and whose members are at the same time part of a web of mutual obligations structured primarily by patron-client relationships.
This is roughly also how the gentry-dominated society of the English colonies in North America worked prior to the war of independence. That is how the Constitution's framers envisioned the new republic would work.