I bet that is exactly would have happened. The reality is that the advance of science and technology and general literacy was quickly eroding the traditional notion of the monarch having the consent of God or heaven.
By the turn of the 20th century this was almost complete, and largely irreversible. From that point on, the only value left in the monarch in industrialized societies was as a symbol of a national ethnic identity for societies that defined themselves in those terms.
Today, only the most extreme religious movements around the world see a return to monarchical society as a goal. Even the neo-fascists would prefer a dictator drawn from their ilk, not a king.
Monarchist countries like the Netherlands, Belgium, Denmark, Norway, Sweden, the UK ... that either stayed out of the war mess or ended up on the winning side were more likely to keep their monarchy.
Prior to the military conflagrations that started in 1914, vast majority of Europeans lived in monarchies, even though the democratization and personal emancipation process was well underway. The only republican countries in Europe at the outbreak of WWI were France, Switzerland and (very recently) Portugal. Well, and San Marino, yes.
If I'm not mistaken, those are also countries that had already significantly diminished the actual power of their monarchs prior to WWI. The UK in particular arguably started that process centuries earlier with Magna Carta. On the other hand, places where the monarch retained the most power, like Russia, saw their monarchs assassinated pretty early in the industrial period.
Today, 80% are still supporting monarchy [1], also among the young [2]
[1] https://www.nrk.no/norge/8-av-10-vil-beholde-kongehuset_-sto...
[2] https://www.nrk.no/norge/3-av-4-unge-stottar-opp-om-monarkie...
The problem for his argument, obviously, is that Hindenburg was the president of the Wiemar republic for the ten or so years that were the meat of the Nazi's rise to power, and he was far more of a hero to the 'strong elements' (far right / conservatives) than the monarchy ever were.
(Obviously, there's a second problem, which is that it's unclear to me if a lack of respect for 'democratic and Parliamentary processes' was the problem with the Nazis. They were voted in, and elections were suspended during wartime, which is normal in a democracy, and were by all accounts very popular throughout the war and after[0]. They also did not substantially alter or suspend the constitution: rather, they used emergency provisions and broadly interpreted resources that were already there).
[0]: Notably, many of the laws they authored, many of the companies and people they elevated or created, went on to successful post-war careers.
"Wise policy would have crowned and fortified the Weimar Republic with a constitutional sovereign in the form of an infant grandson of the Kaiser, under a Council of Regency. Instead a gaping void was opened in the national life of the German people. All the strong elements, military and feudal, which might have rallied to a constitutional monarchy and for its sake respected and sustained the new democratic and Parliamentary processes were for the time unhinged."
I will not quote further but in essence he speculates that in a still young Germany, a monarch could have provided the stability that it came to lack, and which in time lead to the fall of its young democracy. A monarch may not be the right answer always, but sometimes it may very well be.