I think this question has been raised ever since there was something like the French Revolution and republicanism appeared on the scene. Also, the question whether the heir has the ability to become a good monarch is a very old one.
In the 60ies which was a much more revolutionary decade than this many people thought monarchies should be destroyed, Queen Beatrix had the greatest problems when she ascended the throne, in the 90ies even
the monarchy per excellence, the BRF was in question
because of it's elitism. But - they are still here and quite popular. (I really do not agree with other posters here, I think elitism would be the death-kiss for any monarchy in this time of egalitism. People may accept it within the older royal generations, but I don't think they would accept it from the younger.)
Of course there never was and never will be a time when
every single person of a state adores the monarchy, just as not every single person in my country appreciates ("adore" is a much too strong word here) our President.
But IMO monarchies in general are more popular among the younger generations nowadays than they have been for a long time. That might change again, but for now I personally don't see revolutions ahead.
Regarding the Danish monarchy I would say they are quite popular (Not saying that there aren't any anti-monarchistic movements in DK as well). I saw an interview with the editor of the "Nord-Schleswiger", the newspaper of the German minority in DK, on German Tv last year and he said the Scandinavian royals are the most popular among the European royals, and the Danish the most popular among the Scandinavian royals. Don't know how he knows but that's what he said.
And since the queen is probably on the throne for another 15 - 20 years I don't quite see how Frederik will be able to reform anything in the near future (which of course might turn out as a problem for the monarchy).
