I suspect that you will get three different answers for the three different contexts you ask about. That said, the idea, I’d argue, is not to erase the past but to reinterpret it in such a way as to serve the ideological goals of the revolution. I’ll talk more about the French Revolution because that’s the one I’m familiar with. Revolutionaries did not try to pretend as if the past didn’t exist exactly, but they did demonize it. What this did for their regime is it gave them legitimacy by reimagining the Ancien Regime as corrupt and abusive and thus the revolution was legitimate. The new calendar was thus a means of establishing a break with the past that was understood to be contemptible and forging a path towards a new society that was hopefully better.

I’d also like to point out that the Revolutionaries did not reject all history, and that the past societies that they embraced, particularly the Roman Republic, are telling. Revolutionaries immersed themselves in the history of classical Rome in particular. For instance, Robespierre famously said that there were three men in history that he admired, himself, the philosopher Jean-Jacques Rousseau, and Brutus, who betrayed and killed Caesar. There are also a number of famous sociological studies of naming conventions from the 19th century, I’m on mobile right now so I’ll cite them when I’m home, that trace the gradual decline of babies being given Catholic names and, during the Revolution, a trend of babies given Roman names like Gracchus or Cato. So, the past societies which people associated themselves with were very important and got imbued with all sorts of political meanings for revolutionaries interpreting history to serve their own projects.