Anarchists believe that if horizontal power structures are in place, it becomes difficult to go against that current. Ie, if everyone has power, in order to gain more power than another, one must require people willing to give up their power to submit to them in order to push against others. This theoretical group would also have to be strong enough to go against the rest of the public.
It's similar to why Communists believe once Communism is globally achieved, there wouldn't be mechanisms for Capitalism to come back, just like Monarchism is almost nonexistant today.
I'm not an Anarchist, I'm just explaining misconceptions about Anarchism. You ironically lack Materialism in your analysis, with several instances of you claiming hierarchy simply appears, without analyzing the mechanisms of why.
Additionally, society has never been organized historically the way modern Anarchists desire it to be, primitive Communism is not what Anarchists, except for the fringe Anarcho-Primitivists, argue for. Again, they want strong horizontal organization, filled with decentralization. It isn't an arbitrary rejection of organization period.
All in all, I do think you can do better. Rather than simply saying things "appear to organize in certain manners," question the material conditions that changed organizational structures, and analyze why you think specific examples of horizontal organization posited by Anarchists would regress into hierarchy.