Don't mean to resurrect a dead thread, but I've been too preoccupied to address this and wanted to take a swing.
I don't assume that every human is equally prone to corruption, though. But no screening process exists for that. So barring such a screening capability it's the best way to govern groups. Participation of the whole group rather than any select few individuals.
The problem is that you've jumped from a state with corruption to anarchism without considering that there's a possibility for something in between, so you'll forgive me for assuming that you've done so because you believe in the capacity for all humans to be corrupt.
I know anarchism stipulates that the state is inherently bad because a hierarchy that cannot be justified should not stand, but it then (according to the videos you provided) permits the populace to defer to experts on matters which they are trained and practiced to speak to... but deferring to experts IS a hierarchy, as it puts a person's opinion over another, albeit on a narrow topic and with the backing of expertise. So there is room for a state in which expert opinion drives policy and one that can be justified, as one of anarchism's seemingly core tenets already provides the primary justification for it.
I've long been an advocate for a technocratic socialist representative democracy without the influence of parties, as they would no longer be required since they wouldn't unilaterally make decisions anyways. Representatives would be elected to the House to speak to the desires of local populations and propose solutions, which would then be passed to a technocratic Senate, made up of vocational experts, the best of the best elected from within their professions/areas of expertise exclusively, to determine the best way forward to make those desires a reality. Who better to decide environmental policy than environmental scientists? Who better to decide how to approach Medicare than the medical profession? Who better to assist the House with social policy than sociologists and psychologists? Who better to assist with urban planning than engineers? The House would still be necessary, as they would set the priorities based on the desires of each region to be sent to the technocratic Senate, until all priorities are sufficiently met.
And there's no room for corruption there, as parties will have no place; there would be no line to tow since they only set the agenda and don't determine the outcome. As well, vocational voting will mean that if a representative does not adequately address what is in the best interests of said vocation, they would be tossed out exceedingly quickly; when it comes to a person's profession, their passion in life, there's almost no room for politicking and therefore corruption would be easily identified and tossed aside. For example, doctors aren't going to elect representatives for medicine that put their ideology before public health, they have a whole oath that they take that mandates that they shouldn't.
And such a system
could function within capitalism, but to put an end to the "how will you pay for it" boogeyman, it would inherently trend towards a post-capitalism society by necessity. The preference among some technocrats for post-capitalist economies is communal resource/energy accounting, where all members of a population have equal consumption power based on available resources and the energy required to produce goods/services, including the energy required to eliminate environmental damage. To put it more simply, we'd need an economic system that rewards resource efficiency both economically for all citizens AND morally.
You gain all of the advantages of anarchism this way without removing the state, merely changing its functionality. I'm sure you'd say "you can have all of that without a concentration of power to a select few", and... well... maybe? But it requires a leap of faith to do so. Allow me to explain.
Anarchism doesn't concentrate decision making power in the form of a state or representative political class. All decisions are made by local collectives. Economic ones by worker's collectives and political ones
by all people within a given collective. These videos will break it down for you better than I can in this format.
This is where anarchism tends to fall away for me, that it requires all members of a collective to participate and that no hierarchies can exist in order to maintain itself and... I don't have much faith in that, as it would require everyone to be on the same page.
If some abstain from participation, surprise, a hierarchy has just been created! Those who abstain have inherently submitted to the will of another group, narrowing the voices within a collective and thus creating a hierarchy that can't be justified, whether intentionally or not. We see submission to others in our daily lives all the time (a perfect example in my life is the "what do you want to have for dinner" question) and, while disenfranchisement is a major driving factor in abstaining from democracy, there are also those with personal privilege among those who choose not to participate in a democracy, out of ambivalence alone.
One must also consider the hierarchies that would remain in an anarchistic society, despite good intention. Naturally, they would exist at the micro level instead of the macro level, but so long as they exist, they pervert the intention of anarchism from the periphery and could do so with great success. The movement already contends with that before it's been implemented in the form of "brocialists", those who consider anarchism to be something that can exist outside of feminist principles and other measures of equality. Such people would still exist after implementing anarchism, where they could influence society and undermine it by finding ways for hierarchy to insinuate itself.
For example, a domineering husband who pressures and/or threatens his wife not to participate in democracy has thus helped to institute a hierarchy through intimidation. If several of them do so, patriarchy gains footholds. Patriarchy doesn't simply dissolve with the implementation of an anarchistic government, it just goes back to hiding in the confines of one's private residency. Young children reaching the age of majority, likewise, can be similarly influenced through both intimidation and indoctrination to either not participate in anarchistic democracy or participate in a way that upholds the interests of a larger voting bloc.
One could suggest that the simplest way to erode such a plurality of micro-corruptive elements like this would be to institute mandatory democratic participation. But as has been shown in places that have implemented this currently, it is not a deterrent. Part of the reason why is that most of these mandatory voting laws are toothless with minimal to no punishments because doing more than that erodes personal liberty. So, what, you jail non-participants? Threaten them with violence? Those are not solutions, either. In the example of the wife with the domineering husband, threats relating to non-participation just put her between the devil and the deep blue sea: anger her domineering husband and risk violence or disobey the law and risk jail/violence. Some choice.
So much of anarchism relies on the idea that instituting it will provide freedom and cause an enlightenment of the population to all be on the same page, and.... no, sorry, I ain't buying it. Even without capitalism, there will still be means and motives for corruption and hierarchy, they'd merely come from the bottom up instead of the top down. I'd agree that such corruptive influence is better than what we have today, but it's still not good.
This is why I am more in favour of hierarchies constructed to resist corruption on the basis of what humanity would rightfully fight hardest to defend and what is least susceptible to manipulation through fear and greed. In my mind, fear works in current politics because it can be used in a way that does not risk the sanctity of our institutions to do so. If the very legitimacy of necessary professions were in jeopardy because of the actions of our government as they would be in a technocratic representative democracy, you risk all of human society trying to corrupt them in totality and they would thus be defended from corruption to the death by those who have dedicated their life to said professions. THAT is how you resist corruption.
But that's just... like... my opinion, man. And make no mistake, there's so much that anarchism gets right (for example, no "top of the pyramid" through use of rotating delegates to represent regional needs on a larger scale is a really smart idea). But the things it gets wrong are just too important to gloss over or brush aside.