Mussolini acknowledged the King because the King was there, and ignoring him was either impossible or nonsensical.

The Italian Monarchy was older than the Italian State, older than the parties, older than socialism, older than nationalism, older than bolshevism, and much, much older than Fascism. The history of the House of Savoy was tied to that of the Italian State - not only from an abstract, theoretical point of view, but in very practical terms, the Monarchy represented an institution of the Italian State.

As such, there was really no matter of "divine right" versus "the people". Italy was a sort of constitutional monarchy - with a fundamental difference, in so far as the Statute of 1848 was not a proper "democratic" constitutional chart, but an octoryée one, that is a cession of powers from the King to the institutions of the State rather than a document establishing the powers of these institutions by the will of the people. And gratia Dei had Charles Albert granted it. But his son, Victor Emmanuel II, gratia Dei King of Sardinia, etc. had had his ascension to King of Italy sanctioned, by Himself, and approved, by the Senate and the Chamber, "thanks to the Divine Providence and to the will of the Nation". The King had spent his last years partially infirm with the Chamber establishing a praxis of ruling and administering the country, from the elections to the local administration, even wrestling a good chunk of the foreign affairs from the hands of Victor Emmanuel II who deemed himself a strategist and military genius but was quite inept at both. His son, Umberto I had been murdered by an anarchist after a period of social unrest, while the socialist movement was on the rise - a movement which (to quote Crispi) "knew no King, no Homeland no God".

When Victor Emmanuel III had risen to the throne in 1900, he had opened a period of social pacification - personally mindful of, if not really sentimentally tied to, the prerogatives of the Italian Parliament - which had inspired the myth of the "democratic King". At this point, never beloved nor inspiring, but somewhat competent and discreet, most people agreed that the King was the last of the country's problems - first being (the order depending on who you asked) socialism, social and cultural backwardness, the ineptitude of parliament and weakness of the institutions.

Appeals to the divine right of Kings - outside of formal documents and heraldry - would have been quite anachronistic and looked at as somewhat of a joke. Such an oddity for instance was the identification made by G. Papini in 1904 of the Czarist autocracy with the ideal regime, since it embodied the full authority of the State.

Now, neither the kings of Savoy themselves, nor the Monarchy, nor the Italian State were without their blemishes - which means that the idea that the King could be a moron, or the Monarchy outdated and useless, or the post unitary State an unsteady construction, or the Parliament an organism no longer representative of the true nation - in Mussolini's own words "an assembly of morons can't produce a discerning government" - were neither uncommon nor especially esoteric.

These things considered though, as of 1922, a choice between the Monarchy and Fascism would have been somewhat analogue to asking wheter one would rather maintain the US Presidency or Netflix. It's not an obvious choice, even for those who are critical of the institution, which is not accounting for the fact that those critical of the Monarchy were also, very often, critical of Fascism. And the fact that Mussolini - I'd say since his abandonment of the socialist field during the interventionist campaign of 1914-15, but most assuredly since his return to civilian politics in 1917-18 - never put his weight on the anti-monarchical prejudicial, but rather downplayed the issue as soon as it appeared on his way (despite his personal feelings, for cultural formation, education and experience, inclining him towards republicanism), is likely our best confirmation that Mussolini judged any frontal assault against the Monarchy not only dangerous, but quite dumb.

And this is partly because the authority of the Monarchy had not really been shaken by the Great War - or, more precisely, its roots had been weakened by the fall of the last European "autarchies" and the rise of more democratic ideas, but under the circumstances, with "the Bolshevik stain spreading over Europe" (as put by liberal conservative L. Albertini), challenging the authority of the King was really invoking disaster.

And this argument - somewhat instrumentally - had been made by Mussolini himself (according to an informant of the Interior Ministry), pointing out to the last few republicans and anarchists that any step towards a republican transformation amounted to laying the ground for a Bolshevik revolutions.

Which is not, per se, a conclusive explanation, but is at least coherent with the fact that, of the many institutions shaken by the post-war crisis, the Monarchy had not really been one of them. In fact, you'd be hard pressed to find people blaming the King for the "mutilated victory" to any degree - the parliament, the socialists, the bolshevists, the croats, the serbians, the yugoslavs, the Allies, the French, the British, the US, Wilson, Orlando, Sonnino, Cadorna, Porro, the Army, Nitti, Giolitti, Bissolati, Boselli. But not the King - the "soldier King" who liked the life of the "front" (the life of the rear to be fair), sleeping on his camp bed, carrying a few cigars for the infantrymen - he was at the peak of his popularity (comparatively speaking), probably only surpassed with the proclamation of the Empire in 1936.

A tentative debate - on the summoning of a "constituent assemby" - had been promoted indeed, by a composite blend of the formes democratic interventionist forces during the early months of 1919. The project had fallen apart almost immediately, even if it had received some extensive coverage on the press, in part due to the vast disinterest of the socialists who were falling in line with the maximalist positions of the party direction. Anyways the socialists had found an easy weak spot to attack the project, pointing out that the proponents, democrats and democratic interventionists, left unsaid whether this was to be a "monarchical constituent" or not - "a consituent with anyone, which means with the monarchy as well, especially with the monarchy".

For his part, Mussolini further diluted (intentionally or mistakenly, depending on whom you ask) even the idea of a democratic constituent by invoking instead a "constituent the interventionism", which was to be opened to the nationalists as well (or not?).

But again, there seems to be no special attention to constitutional programs, democratic reforms or anything truly challenging of the Monarchical institutions in Mussolini's works during 1919-22. Which is not surprising given Mussolini's general take on institutions and their general public perception - them being serviceable, instruments to be used or forces to contend with; the first one if possible. After all, Mussolini's coexistence with the King lasted twenty years despite his republican inclinations; his anti-clericalism didn't prevent him from settling the long lasting disagreements between the Italian State and the Holy See.