The confusion is all yours, John.
When at war, nations unite behind their leader, whether president or prime-minister.
Yet presidential elections can severely undermine a nation, creating division because the winner-took-it-all. Acts of war can break out when the loser lost just with a handful of voters (or better: perceived the election as a stolen win).
Presidents or prime-ministers can do the exact same leading. Yet presidents are elected in divisive manners, while prime-ministers are always resulting from a majority deal supported by a clear majority of the voters.
But it gets worse, see the next graph from 2006.
You can see that nations with a president can potentially do as great of a job for their poor as those countries without a president. Yet you can also see that nations with a president can sweep the floor with their poor like no others.
The US gives 1.8 percent of its national cake to the bottom ten percent of society. Denmark: 3.8 percent, all because Denmark has A: No President, B: Full Representation, and C: One House and One House only. The Danes are empowered as voters. We? We have voters compete with voters for the win of House, Congress, and Presidency. If you were lucky enough to pick the winner three times, then still these three outcomes can end up fighting one another, all of them saying that you gave them their power.
The Danes are empowered in the voting booth.
We? Not that much!
https://data.worldbank.org/indicator/SI.DST.FRST.10
Just look at Denmark, the Netherlands, UK and USA on this list. Winner-take-all is a divisive system that ends up being good/okay for the majority, but not for everyone. A president is always winner-take-all of course.
