Um, I don't think so. Conflict resolution is the main obstacle to the viability of entirely voluntary ("anarchist") organization. That's why it's the self-defining function of any government, even the most minimal.
Because for me, outside some formal processes I do for my job, it has been well over a decade since I needed someone to mediate my interactions with someone else.
People are very good at conflict resolution. They only see the cases where it doesn't work out.
Business still gets done. People work, get paid, buy things without knifing each other. It is true that without recourse to state institutions, there is more non-state-sanctioned violence, which is kind of definitional, but also true in absolute terms.
But enormous amounts of daily interaction goes on with humans demonstrating perfectly normal abilities to compromise without killing each other.
This is another form of 'elite panic' - the belief that The Lord of the Flies is just around the corner if Officer Smiley stands down. People don't behave that way in reality.
Second, you somehow think "scary place hurrr silly anarchist just doesn't want to admit..." is a killer argument. It is just slightly recast version of the "If you like communism so much then move to Russia" schoolyard silliness.
If you want to discuss how political theory intersects the real world, I love that stuff. If you just want to convince yourself anarchists are dumb, that's boring and I'm out.
You're not really selling your case very well here...