I will do a couple of follow-up posts to this one.
As I've written in that post and others, the most significant role for a head of state in a parliamentary system is to appoint the prime minister. But only the parliament, via a vote of no confidence, or the electorate, via an election defeat, can remove the prime minister from office. In other words, the severe limitation on the head of state's power in this regard is that he or she can hire, but not fire, the prime minister.
If one party wins a clear parliamentary majority in an election, the designation of a new prime minister is a mere formality; the head of state must give the job to that party's leader. But it is when things are more messy than that, that the head of state's role can become more interesting.
In the aftermath of World War I in Germany, the political situation was constantly messy. Economic problems brought on by the war, and by the terms of the Versailles Treaty that ended that war, made for an unstable society. And a high degree of proportional representation in their electoral system prevented any strong government from emerging.
In November of 1932, a German general election gave the highest number of parliamentary seats to the National Socialist German Workers Party, although that total was well short of a majority. You might not recognize that party's full name, but they were better known as the Nazis.
The German head of state at that time was President Paul von Hindenburg. The president, a career military man, might, earlier in his life, have been strong enough to prevent Adolf Hitler's rise to power. But, by January of 1933, Hindenburg's best days were behind him; he was 85 years old, and less than two years away from death.
Hindenburg appointed Hitler as chancellor, which is the title the Germans give their prime minister. Hitler immediately began a series of steps to consolidate his power and eliminate German democracy. He, of course, held on to dictatorial power until his suicide, shortly before Germany's surrender to the World War II Allies.
Now, it might be a kind of retrospective wishful thinking, to believe that any German president would have been able to stop Hitler under those circumstances. But that is just the sort of scenario in which, ideally, a head of state would prevent a head of government from destroying democracy. It's somewhat analogous to the Spanish example I mentioned in the previous post in this series, when King Juan Carlos prevented a coup from supplanting the nascent democracy in his country.