A republic, or an oligarchy by any other name, even one ruled by law, is a notoriously indecisive form of organization. I do not see a better division of labor than the one we discovered by accident.
A republic is an excellent means of producing commons. A monarchy an excellent means of conducting war. And a democracy an excellent means of fooling the people into suicide.
The Optimum that I know of:
1) Monarch, Military, and Militia for the defense of people, territory, routes, and trade.
2) Independent Judiciary for the resolution of conflicts, Rule of law, Property en Toto.
3) An independent treasury for the provision of credit (issuance and repurchase of shares)
4) Houses for the Production of Commons with members drawn by lot.
5) Families for the production of generations under voluntary selection of mates.
6) Men and Women forming Militia and emergency services.
7) Private provision of public goods.
We had it about right. If we had given women and the proletarians houses and maintained land and property requirements we would have created a market for commons, instead of the fallacy of majority rule (mob rule).