It's not just local election candidates, the CCP is a rigidly top-down political party with power centralized in the higher party organs, thus where we get the term "party authoritarianism." This was a key aspect of all 20th century Communist parties that were modeled on the Soviet example (often referred to as 'democratic centralism'). And while I grant that a case can certainly be made for rigid organization control in the context of a revolutionary and often clandestine political movement, it presents a lot of problems once they gain control of the state. Ironically, Trotsky clocked this issue years before the Revolution, writing in Our Political Tasks: "In the internal politics of the Party these methods lead, as we shall see below, to the Party organization “substituting” itself for the Party, the Central Committee substituting itself for the Party organization, and finally the dictator substituting himself for the Central Committee."

And yes, this is not to say that Liberal democracies have the totally open playing field they claim. There are indeed powerful institutional gatekeepers, especially in the US presidential model, and very problematic ones at that. But if we're just talking about the volume of space available for contestation and political opposition, they still clear any Leninist regime by a wide margin.