Rule of Law is Rule of Law ( prohibitions, via-negativa ) regardless of the form of Government (actions, requirements, via-positiva). The only necessary function of law is the resolution of disputes. The only necessary function of government is the production of commons. In a democracy individuals vote on those commons recommended by whom? A king? A bureaucracy? Any proposed by anyone? In a republic, individuals vote for representatives who then vote on those commons. Dictator/Monarchy, Cabinet, (Representatives) Bureaucracy, People.
European Parliaments like thangs and juries were originally juries, where the monarchy would petition local landowners (businesspeople) if they wished to tax them for some purpose or not. The battle over via negativa control Rule of Law vs Rule by DIscretion), and the limits of exception on rule of law vs rule by discretion, and the distribution of via-positiva rule between monarch(nation)/dictator(empire), oligarchy/parliament (intermediary between state and people), and the people, has continued.
As far as I know the form of government is dependent upon the demographic distribution of the people (relative sizes of the classes), their state of development (size of the middle classes), scale of territory, and hostility and competitiveness of neighbors.
If we want an ideal government – at least, the one possible by man – we probably had it: small homogenous nation states, rule of law by the natural (necessary) law of reciprocity (tort, trespass), an hereditary monarch as judge of last resort, a cabinet of professionals acting largely as venture capitalists, a small professional bureaucracy, preferably trained in the aristocratic (private secular), church or confucian model from youth. Via Negativa voting by the people in matters of taxation. And (what is causing most of our 19th-20thc problems) universal standing before the court in matters of the commons.
This creates a political market for commons, a productive market for goods services and information, and a juridical market for prosecution of ir-reciprocity regardless of whether private or public.