Works OK for countries with parliamentary democracies.

Parliamentary democracies still have distinct executive branches.

Sure, but they are usually appointed by the majority party of parliament and its leader becomes head of government.

No, that's how a dictatorship works, not a parliamentary democracy. The prime minister/head of state may set policy, but it's still subject to an up/down vote in the parliament. In all cases I can think of, a prime minister can't unilaterally make such drastic changes without (parliamentary) referendum.

The U.S.'s federated system just makes it more explicit what's going on.

The above isn't meant as a comment - it was a question that was answered by an edit in the grandparent, but I then carelessly edited this instead of deleting it. By the time I noticed the error the edit/delete window had closed.