Good try trying to use your diabetic child as an excuse, but, and it saddens me every day that this is the case, there aren't enough doctors to go around even among the developed nations, and many of them are choosing to go where they're being paid the most. People with illnesses and health conditions are being propped up by this system. Unless the whole world switched over at once, your kid would not be able to get the medical treatment they needed unless you outsourced back to those doctors. Which is a conversation that Trotsky and Stalin had a hundred years ago, so we aren't exactly paving new ground here.
Also, yeah, you are suggesting Communism. The idea of property and the means of production being used for social control and needing to be removed is extremely Communist. I have nothing against Communism, though.
You can't have a large scale society without authority. You can't even have a small-scale society without authority. We will pick out a leader just out of habit. I can tell you exactly who the leader is among my D&D players, the students in my department, or in my circle of friends, even though none of these are formal institutions created to delegate labour. Hell, even if it was possible, who would be administrating the distribution of all these goods world-wide?
My kid needed a doctor once. To be diagnosed, and to teach us how to care for him. Now all he needs is insulin and synthroid. However the concept of property naturally leads to the greediest among the population being in control of the production of these medicines and demanding greater in return than it took to produce them. The specifics of how those medicines would get produced and distributed in anarchy is an argument mostly hinging on personal opinions of human nature, making it basically pointless to debate. I'll only say that I think our current paradigm corrupts human nature, and that it would be much more providing when set free of this paradigm.
While my criticisms of the current state of things sound much like the same used by communists, I do not promote communism as the solution. That would imply centralization of resources into the hands of a few (the state) who retain control over them by force and distribute them according to their judgement. In the best-case scenario, the state is made up of people selected by the population, which leads us to politics and we all know what kind of people win in politics. To me, this is no different from the end result of capitalism.
I don't have any specific vision of how society should operate, mostly because I think this should be left up to every grouping of people to decide for themselves and partly more because my ability to envision life outside of our current paradigm is so limited. I'm living in the dark and all I know is that I see the dark for what it is and I know that there is light.
If I had to label my ideals, I could only offer mutualism. I think that left to their own devices, people would pursue their own interests. If people want food, they'll do what they need to produce food. If enough people want electricity, they'll organize to produce it. They may not live in as much material excess as we know, but the luxuries they have will be those they produce for themselves rather than those they produce at the whim of an authority figure and will inherently provide greater fulfillment.
I think the only economic model humanity needs is as follows
1. If you have more than you need, share.
2. If you don't have what you need, find some one who can share.
3. If no one is able to share, set about producing it.
4. If you can't do it alone, get help.
As for large scale society/authority... I would have agreed with you 20 years ago. With mass communications where it is today, I disagree. I do agree that people pick leaders out of habit, but that's a tricky subject. How much power do people give a leader appointed out of organizational convenience? Typically not much, I'd wager, and less as time goes on and means of communication as equals becomes more widespread.
For instance, if the leader of your D&D group demanded something unreasonable of you and threatened that everyone else in your group would act violently towards you if you don't comply, would they go along with it? Yeah... I don't think he's the type of 'leader' that I'm complaining about here.
Above all, I think we accept leadership where it exists coercively only because we're swimming in it from birth and either as oblivious to it as a fish is to water or are doomed to be just one voice surrounded by oblivious fish. Other cultures without such violently centralized hierarchies of authority have typically been really really really resistant to the imposure of such. In fact this centralization of resources and authority has only been typical for a very very very miniscule portion of human history and has proven itself to be very unstable in a relatively short period of time (I hope I don't need to argue the current instability of the modern world).
I think it's very much against our nature, which is why so many of us can't agree about how it should be done and why so much of our culture passed on through the ages bemoans feelings of meaninglessness and emptiness and so goddamn many people take anti-depressants just to be able to cope with day to day life. As far as I can tell, indigenous people rarely exhibit such symptoms, because they're too busy living their lives to an extent that the common modern day civilized person is denied.