The fundamental problem here is that you still have the same problem any monarchy has--much depends on the personal character of the monarch. When kings are expected to rule more or less absolutely with parliaments or noble councils being adjuncts and perhaps somewhat checking it, but the monarchy is itself still the center of government, then there are frequent plots and intrigues to make weak kings into puppets or usurp the crown completely; the fact that a faction might make a king into a mere figurehead is not that different from the alliance of factions a strong king would organize and maintain.
But if there is some body comparable to a parliament in the modern European sense, of a broadly elected body that a large majority of the population can elect the members of and which holds the balance of power normally, so that the nation can be said to be a democracy of sorts, what are the odds that the nominal monarch will have any talent for managing the nation better than such a body could manage to on its own without royal help? If the parliament has evolved to the point that it is competent to govern but comes to this condition in conjunction with a line of highly competent monarchs, for a time a mixed constitution will exist and seem natural, even a stroke of national genius--but sooner or later the king will get out of step and then either the royalist party must abolish the parliament or anyhow reduce it to impotence--or the parliament must check the royal power if not abolishing it completely.
FWIW, I do suspect the maintenance of the apparently ceremonial monarchs typical of much of modern Europe do indeed represent a possible contingency of return to dictatorial rule in their name, a fall-back position in case of "national emergency." But the sort of emergency that would lead to their resumption of monarchial power seems increasingly far-fetched, except for circumstances that would probably amount to most of the nation being dead.
I have on the other hand imagined the possibility of a canny royal line taking an analytical look at the transformations of society happening in the 18th and 19th centuries and, instead of either succumbing gracefully to the tides of bourgeois forms of democracy and retreating to a ceremonial role, or stubbornly trying to cling to a past where they were essential on old terms that leave their realm increasingly bypassed by modern developments and vulnerable to the upstart bourgeois-parliamentary nations, instead reinvent their royal house to claim kingship over the nation as a whole, strategically seeking to pre-empt radical democrats by championing certain interests of the commoners against the rising middle classes. If they can make the parliamentary movement one limited to the bourgeoise itself and the old nobility, while presenting themselves as defenders of the poor and working classes, they might pre-empt the inclusion of these lower commoners in the representative bodies, making the royal institutions indispensable as referees between capitalists and working people. Thus, they can open the nation up to capitalist development which however the royal institutions govern and guide according to a more or less scientific development plan. By selectively recruiting talented commoners from humble origins into royal service and developing a monarchial bureaucracy acting in the name of the king, perhaps the monarchial power can perpetuate itself in counterpoise to a representative body that is universally seen as representing only the privileged classes.
The pitfalls of such a scheme would be many of course; the natural tendency of the king (or queen) and inner circle of high-level royal servants would be for them to identify with the rich and powerful, the most successful business leaders and the old nobility that is to say, and then populist discontent would naturally tend to see them all as one and to either overthrow them all together, or infiltrate and coopt the whole edifice to more democratic purposes.
I gather to some extent many new dynasties have some tendency to play this game of "king and commons against the rich SOBs" and that Louis Bonaparte aka "Napoleon III" based his power to some extent on this very mystique (if not so much among urban proletarians, than strongly in the countryside among the peasantry). These examples show how it is an unstable and transitory thing; for it to work for generations and be sustained, the monarchy would have to maintain itself distinct from the aristocracy and stick to a plan passed down by careful education of each generation of heirs. The royal bureaucracy might carry the system through the reign of a weak monarch--but if the dynasty does not produce kings or queens who can inspire the masses with their indispensable benevolence and shrewd, wise yet bold decisionmaking that reliably proves sound in the long run, then eventually the royal institution will be called into question, in favor of a merger with an expanded-franchise parliament or the takeover of the dictatorial bureaucracy by insurgent radical democratic forces instituting scientific socialism in the name of the people directly.
Some kind of alliance with religious authority is probably necessary to maintain the sort of modernist philosopher-kingship I'm talking about; the king's own bureaucracy would probably have to be largely staffed with some kind of clerics and his do-gooding among the common people presented as the king doing God's will via humbler servants of God.
I've suggested the notion for various timelines that the Hapsburgs might revitalize themselves along these lines in attempting to hold and develop Austria-Hungary, with the help of a Catholic order or three doing the investigative, administrative and ideological work. I've also wondered if other German monarchs of the 19th century might have tried this path.