I want to say first that I hope to leave aside for now any question of whether Stalin's Russia, Mao's China, the Kims' North Korea, etc. are "really" Communist or actually something else; that's a subject that seems to derail any thread about this sort of thing, and I'm just not interested in it here. I'm asking about those nations that have really recognizable shared cultural-political-aesthetic attributes, which have all claimed to be communistic, and which have all been called communistic by both their allies and opponents. I hope that's alright.
So, what is the deal with this, exactly? Why have we seen such a wide variety of cultures suddenly going over to public aesthetics that involve giant portraits and posters and statues of living people, that involve millions of copies of small books containing choice quotes from certain leaders, that seem to see the rulers of these nations take on (in some cases) almost a quasi-divine authority? It all seems very much at odds with what's going on with the rest of their politics and I have to admit to it seeming way more weird to me for there to be gigantic heroic iconography of "secretaries" and "speakers" everywhere than to have the same kind of thing for an emperor or a king.
What made me ask this question was coming across a copy of Mao's little red book, which is basically a collection of quotes by the Chairman on various situations and ideas. I was struck by how unlike it was to anything else I'd ever encountered outside of an ancient religious text, and also, if you'll forgive me, how absolutely boring and unuseful almost all of the quotes were. What was it about something like this that was felt to be so important that hundreds of millions of copies of it have been printed to distribute around the world?
This is a sort of long odd question, and I will gladly withdraw it if it's inappropriate. I'm not sure how to put it more briefly than the above.
I'd question the basic premise of the question: that Communist dictatorships are any more prone to cults of personality than any other form of dictatorship.
There are more than enough non-Communist dictatorships to note. Africa alone offers Idi Amin, Jean-Bédel Bokassa (both particularly grotesque examples), Hastings Banda, Gnassingbé Eyadéma, Mobutu Sese Seko, etc. Plus a whole host of mere 'fathers of their nation' and other exalted presidents. Nor is it hard to find examples of these cults further afield: there have been plenty of 'giant portraits and statues' in the Americas, Middle East or Asia (eg, Hafez al-Assad and Saddam Hussein, François Duvalier and Rafael Trujillo). In this context Communist states are perhaps most notable for pioneering the modern form of the cult (ie Stalin) and occasional denunciations of it (eg, it was Khrushchev's popularisation of the term).
So why do cults develop anywhere? Milan Svolik (The Politics of Authoritarian Rule) frames the cult as part of what he terms 'authoritarian power-sharing'. That is, the interplay between the dictator and the rest of the governing elite. So while the latter attempt to limit the dictator's powers, via the use of institutions, the cult aids in elevating him above his peers: making clear that he is an 'established autocrat' who rules without constraints. Stalin is, as so often, the archetypical example: the development of his cult proceeded along with his rise from junior Politburo member to first amongst equals to absolute master. Svolik argues that this applies to all dictatorships as they lack democratic institutions capable of mediating between competing factions.
In which case it's not the content of Mao's 'little red book', for example, that mattered but the fact that it's distribution publically promoted Mao at the expense of his CCP rivals. The cult was part of Mao's campaign to overturn the party structures that restricted his personal power. (Not that all this may have been conscious at the time.) Note the lack of such overbearing cults in today's China, where CCP institutions are designed to prevent the emergence of a single undisputed dictator.
(It's worth noting that this occurs at all levels of the state. Local personality cults emerged throughout the Soviet Union in the 1930s as regional bosses created their own patronage networks. Sheila Fitzpatrick's Everyday Stalinism contains a good/vivid summary of this.)
I disagree with Svolik on a few points but like his core thesis on this issue. It helps explain why cults are common enough to feature in strongmen military dictatorships and also party-based ideological dictatorships; why their prominence within a single country can vary dramatically within a generation. In this Communist regimes are little different from any other – the same dictator v elites dynamic is at play.