Ah, one of my most vivid memories of taking a university course
in some category of government history.

The subtle and wry professor presented the paradox with the polish
of someone who presents it every term, rain or shine. He said:

The majority of first-world countries have a head of state and they have a head of government, and they are two different people with two different jobs.
For example, the constitutional monarchy, which has a queen or a king, as the head of state,
and also has a prime minister as the head of government.
Another example,
the country which has a Madame le premier ministre, that is when le premier ministre is not male for a change,
and has a President who is the head of state.

You know what's odd, the professor said?
The United States only has one individual as
both head of state and head of government.
The other first-world countries aren't like that;
the other countries that have one individual doing both functions
tend to be dictatorships

--pregnant pause:
"But that doesn't mean anything."
Swift change of subject,
and I sat there, in the back of the classroom,
with red lights flashing in my mind's eye.

It rings ominously true today.