I don't think so, too much freedom will absolutely bring chaos. Even though some of the governments control our moves, we still need them to keep the society more livable.
The thing about it is, the world would still function, it just wouldn't be as organized. There would be a ton of chaos, and anarchism isn't exactly sustainable, it's in human nature to form societies so over time you'd see governments form again.
I would just add that people always need a leader, someone who will take a responsibility for their decisions. Besides, our brain is made up in such a way that we strive for organized structure.
People who support anarchism are just tired of the existing government.