The English civil war in the middle of the 17th century was about where the power would like: With the executive (king)? Or the Legislature (parliament)? So, as I said, the system is pretty simple and easy for the US to "adopt".
It just comes from the admission that the power to run the government, as in making laws and that lies in the legislature. The legislature is the body which is the closest to the people. This is why I like it.
It's easier for a third party to gain traction locally than nationally: especially with the current duopoly in power. Likewise, having a true multi-party democracy will require that there are compromises. This is in contrast to the ultra-partisan bullshit in the US. Coalitions need to be formed.
Or a new election is called.
Sure, this may show up the US for the disunited states that it actually is, but those would be better teething pains than what is happening now.
The executive does what it should do: run things. It's the career civil service who administer the government.
And the courts can do what courts should do: decide legal cases like umpires in a game.