The rest of your post is great but this point is not accurate, at least according to PEW, there's 33 countries with a combined head of state and government (as in the U.S.) that elect that person by direct popular vote:
http://www.pewresearch.org/fact-tank/2016/11/22/among-democracies-u-s-stands-out-in-how-it-chooses-its-head-of-state/ft_16-11-21_headsofstate_bar/
All countries with the British model (UK, Australia, Canada, etc.) plus most of Scandanavia have parlimentary systems with a figurehead monarch, so obviously aren't counted amount the 33.
Those within the 33 range from places like Mongolia and Turkey who have sham parlimentary systems elected simultaneously with the national leader who automatically wins when the party wins to more normal parlimentary systems who follow a similar pattern on the surface and don't allow the voter to pick, for example, a leader from one party and a legislator from another. So yeah, they are voting for the head of state in a direct sort of way when they choose their parliment. But there is a huge difference between their parlimentary versions. The national leader or strongman in, say, the Turkish system really owns the legislators. Under the Polish or Finnish system, they are just the head of state which the legislators can and often do turn against when the winds of politics shift.
This is also the rule in the figurehead monarcy systems such as Canada and Japan.
The stupid PEW chart does nothing to separate this reality and has an agenda of isolating the United States by presenting facts in this warped manner. Remeber when Saddam was in power in Iraq and the mainstream news was treating an election there as an actual election with an uncertain outcome?
The truth of the matter is that our electoral system has far more in common with the parlimentary system in Finland or Poland than these countries have with the parlimentary system in Mozambique or Turkey. And still more in common with figurehead monarchical systems such as Canada or Australia, whose only distinguishing feature is (a)they have a figurehead monarch and (b)their legislature chooses the head of state.
For example, it is theoritically possible for Canada's voters to sweep out Justin Junior's party and for the new parliment to vote to keep Junior as head of state. The chances of such a happening are, of course, near zero.
Remember that PEW is an organization with an agenda.