Your entire ideology is based on a completely flawed foundation and literally all of history, logic, and science proves you wrong.

When you're being this shallow with your questioning, the same criticism can be made of liberal-democratic systems. To describe my own flawed understanding simply (I have not read any historical anarchist): I don't see an anarchist society as necessarily being in many ways functionally dissimilar to liberal democracy, but instead of spending the majority of it's energy mediating the class-conflict between capital and labour, with really smelly compromises that nobody likes, it would have won the class conflict, and now expend that energy solving the conflicts arising between different individuals' needs, and those of the communities.

Asking how to solve specific problem with doctors XYZ isn't remarkably insightful because solving that problem is a process an anarchist society operates specifically to solve. That is to say, the whole proposal is a matter of shifting the principles of moral or ethical governance from weighing different sides of the class conflict to solving conflicts between individuals and communities with equal stakeholdership in the means of production and equal right to having their needs met. The koolaid is already deep in the inherently flawed capitalist system, where there are obvious areas that conflict and contradictions exist; it's exactly where these arise that the political system steps in to fabricate a solution to the crisis; but now in contrast to anarchist principles, under capitalist principles it's all done while letting the top still shit on and all over you.

I mean, i don't see how my answer is in any way really helpful, because it's just "we'll figure it out;" but i mean, the corollary in the capitalist system is asking how do you, how COULD YOU, EVER deal with poor children starving? Right, we figure it out, often with social programs now; that operation or mechanism of figuring shit out doesn't go away, just the rich and powerful people.