Why did totalitarian leaders like Hitler, Stalin, and Mussolini encourage popular involvement in particular artistic styles?

All three dictators looked upon art as a means to an end: to enhance their power and to serve their respective regimes. They all recognized the enormous propaganda value that works of art could have for totalitarian regimes like theirs. Both Hitler and Mussolini advocated for a neoclassical aesthetic, one that drew from a heavily mythologized past. This approach complemented the Nazis and the Fascists' fanatical belief that they were recreating the greatness of glorious empires.
Stalin, for his part, used certain aspects of Socialist Realism to help further the Soviet regime's message. Socialist Realism, particularly in relation to drama and the fine arts, displayed an idealized image of the heroic working classes leading and sustaining the heritage of the Revolution, acting as the vanguard for the movement toward total Communism. Their commitment to the Communist cause was presented as being pure and unsullied, an ideal to which all must conform.
All three dictators understood that popular forms of art were more amenable to being used as vehicles for propaganda precisely because they were popular. Popular forms of art had a deep appeal to the masses the totalitarian leaders wished to control. At the same time, there was systematic state censorship: any kind of art that was deemed radical, abstract, or challenging was ruthlessly suppressed, as they could not be adequately controlled.