Is the general wisdom that the executive function should be a separate co-equal branch of government (like the US), or controlled by the legislature (how I understand a parliamentary system)?
Contemporary general wisdom is that parliamentary systems (executive subordinated to the legislature) do better than presidential systems (executive and legislature are separate and co-equal branches of government)
It is worth pointing out though that you can have a parliamentary republic in which the President has very limited powers in practice and most of the real power belongs to the Prime Minister - for example, Austria, Germany, Ireland, Israel, Italy, Malta. Monarchy-vs-republic and presidential-vs-parliamentary are (at least partially) orthogonal
There is also the semi-presidential system used in France, and a number of other countries, in which control of the executive is shared between a directly elected President and a Prime Minister chosen by the legislature. Often, the Prime Minister has more power over domestic affairs while the President has more power over military and international affairs. Sometimes they can be from opposite parties which can cause difficulty. It is half way between the parliamentary and presidential system.
I life in a parliamentary syatem, and branches, all of them, are equal. In pratical terms, there is some overlap since people in the executive tend to be pretty powerful in the legislative as well. If you take France, with a pretty strong President, even the president needs the legeslative to pass laws, he can't order them around.
By definition, in a parliamentary system, the executive is de facto subordinated to the legislature, even if they may be theoretically considered equal. If the executive and legislature are equal in your country, not just in theory but also in practice, then you do not live in a true parliamentary system, even if some might call your system “parliamentary”.
You mention France-as I said, France does not have a true parliamentary system, it has a semi-presidential system. In a semi-presidential system, the executive and legislature are more equal than in a true parliamentary system (in both theory and practice), albeit not quite as equal as in a true presidential system such as the United States.
I think the argument is that a powerful Prime Minister is not really subordinated to parliament- that Merkel does not, in practice, really answer to the party, but instead the party answers to her. I am not personally making that argument, but I think that's the response- that there's a difference between how parliamentary systems work in theory, versus in practice
> I think the argument is that a powerful Prime Minister is not really subordinated to parliament- that Merkel does not, in practice, really answer to the party, but instead the party answers to her.
Merkel always governed as leader of a coalition - mostly a “grand coalition” with the traditional main left-wing party (the SPD), although her second cabinet was a coalition with the classically liberal FDP instead. So, forget about answering to her own party - if at any point her coalition partners had felt it was in their political self-interest to do so, they could have collapsed the government.
I think this argument is really drawing on the fact that Merkel was genuinely popular with the German electorate, which protected her against any desire by her party or coalition partners to push her out - they knew the electorate would punish them if they tried.
But, true power does not depend on popularity, it continues even when people don’t like you any more. A US President may become despised by both Congress and the voters, yet to remove them before their term is up, Congress needs to allege actual wrongdoing (as opposed to just “we don’t like you any more”) and needs a super-majority. By contrast, an unpopular German Chancellor can be removed by their party and/or coalition partners, before the end of the electoral term, without needing any parliamentary super-majority or specific allegations of wrongdoing. In that sense the German Chancellor is subject to the Bundestag, to a much greater extent than any US President is subject to Congress.
