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  Yes, that’s why I used the term “leader of the country” rather than head of state or head of government. And I never said a parliamentary has zero separation of power, rather that an executive branch should exist, and be separate from the legislature to increase the separation of power.
  As for your third point, which system you prefer is irrelevant to which is more democratic. More democratic doesn’t always been better, and you’re welcome to think a less democratic system produces better results.
context: Well first off, the POTUS office isn’t one-to-one with a prime minister of a parliamentary democracy. The POTUS is the head of state in the US, whilst the head of state in, say, the UK, is the king. The prime minister is just the head of the government, and is much more restricted in terms of executive orders and such than their American counterpart. 
  Secondly, you seem to think that parliamentary democracies don’t have separation of power. They do, just as the US. The government is separate from the parliament, just as in the US. 
  Thirdly, I think you place too much important on individuals over parties and policy. I don’t necessarily care who heads the executive branch, I care about the policies they enforce. And that’s much more dependent on which party they represent than who they happen to be.