I agree that a day without government would not happen over night. There are going to be essential functions and services and social safety nets provided that could not or should not go away. Those are the things that I think would cause the chaos that you mentioned.
I would advocate for moving those essential services and functions to a true free market, privatized model. There are already cities doing pretty much what I would advocate for at least transitioning into which would be privatization of services normally provided by an incompetent, expensive, monopolistic state. I would like to see more cities start doing this, showing people the uselessness of government.
You should check this out:
https://liberty-intl.org/2014/06/the-town-that-privatized-everything/
I hope as well that we can get there some day, but I am not holding my breath. We have a lot of work to do as probably already know :)