The problem with anarchy is that everyone must be a good anarchist for it to work. Our current society is also dependent on most people being good anarchists, but it's also more resilient against non-anarchists.
Also, removing state power structures will not remove all power structures. There will still be people with lots of material or social capital providing them with power.
My hunch is that in absence of laws and power structures most people will miss a social contract and will miss people telling them what to do. Basically it's less taxing on our minds.