Why aren’t there any countries with a directly elected prime minister? Israel tried it (incompetently) but beyond that it is only talked about (the Netherlands, Hungary, Japan) but most republics have a directly elected president, and yet most constitutional (symbolic) monarchies, still have the prime minister’s authority rest with a majority in the lower house. So called parliamentary government. In this system, the lower house of parliament (or just parliament in a unicameral system such as Sweden) holds legislative power as well as the source of executive power, since it controls the government/executive.
This makes me think of the words of Montesquieu:
But if there were no monarch, and the executive power should be committed to a certain number of persons selected from the legislative body, there would be an end then of liberty; by reason the two powers would be united, as the same persons would sometimes possess, and would be always able to possess, a share in both.
The Spirit of the Laws, vol. 1, trans. Thomas Nugent (London: J. Nourse, 1777), pp. 221-237, passim.
Parliamentary government means there is no real separation of the executive and legislative powers. When a powerful executive ruler appoints parliament this is viewed as dictatorial, but the reverse is treated as perfectly acceptable. Why? The former is indeed watered down elected autocracy, but the latter is watered down elected oligarchy. The idea behind a separation of powers is to prevent abuse of power by either one elite body or one elite individual (whether elected or otherwise).
Parliamentary government is the democratic form closest to elective oligarchy. Politicians who don’t get the support of the party leadership of a leading party will never be prime minister. The ability to negotiate with other parties (party leaders) is more important than broad support amongst the people. It attracts people who are good at getting along with the elite.
The entanglement of powers in the parliamentary system leads to complicated powers struggles between party leaders. Forming a coalitions is always an all or nothing contest. The majority coalition ends up holding both executive and legislative power. Again confirming that this is the opposite of a trias politica. Powers is too centralised within the coalition. The government depends highly on stability within the coalition. As a result the most succesful parties are those which are able to enforce the strictest party discipline.
Other problems caused by this system include hung parliaments, as well as the need for new elections when a coalition breaks up. These all or nothing formations can last very long.
Prime ministers aren’t bound by term limits the way most presidents are either.
Quite frankly, parliamentary government is the worst form of democracy and one of the worst forms of government period.
Hung parliaments don’t exist in a presidential system. Instead the lack of a majority party in parliament leads to the need for across the aisle negotiations, census and compromise.
A directly elected prime minister could function similar to the president in the US or Brazil, a presidential system, where the elected prime minister appoints other ministers and leads government policy without parliamentary influence. This would be close to a strict separation of powers.
It could also world in a semi-presidential form where the ministers appointed by the prime minister can still be removed by a vote of no confidence in the lower house. This would still leave parliament (legislative branch) with some influence over the executive, but as long as the prime minister could ordinarily veto legislation, there would still be a balance of powers.
Either system prevents the various problems of parliamentary government.
If you wanna be original, you can add the feature than the elected prime minister can still be removed by a vote of no confidence, but then one which needs 60 % support of all the members of the lower house. This would result in a new election. That way terrible deadlocks could be broken and there would be a check that would prevent an overly authoritarian elected prime minister. Parliament might (mostly certainly would) be more inclined to oust a prime minister they didn’t bring into power in the first place.
Regardless, let’s stop pretending as though parliamentary government has a tripartite separation of powers, it doesn’t, it merely has the appearance of one.