Why do you think that the market should yield to spontaneous mutual aid?

When I say "should", I mean in the sense of an imperative. As in "You should brush your teeth before going to bed" not "The bus should be here in 5 minutes". It is the intention to drive the market towards spontaneous mutual aid through post-scarcity.

As to the how, I specify market socialism as an initial intermediary step. Collective ownership, even limited to the firm level, inherently counteracts wealth concentration by distributing profits between the worker-owners. Maximizing worker-ownership is the primary focus. Eventually, abolish the stock market entirely and replace existing stocks with bonds.

From there, as automation prevails (with profits settling more equally) the work week will get shorter and shorter and production cheaper and cheaper until it basically isn't worth the trouble of keeping track anymore.

I get the skepticism, but socialist markets have fundamental differences from capitalist ones; the primary difference being wealth concentration.

Anarcho-communism isn't against stepwise processes, but our critique of state socialists is that the State is structurally incapable of bringing about communism within any time bound.

Which is why I'm presently a market socialist, not a state socialist. The state is just another centralized hierarchy. Businesses are distributed. Parallel to the economy, the next social step is community development, and flattening of hierarchies through densely iterative representation. Don't get me started.

What we mean is that the solutions we pursue should reflect the values and priorities of the world we actually want to see.

Which I respect, but when pursued beyond the context of the material conditions of the world in which we currently live, those values and priorities can be taken to the point of impotent ideological virtue signaling. We're wrestling pigs here, and if we're preoccupied with keeping our shirt clean then we're not gonna make much progress.

Since we want to see a world without hierarchy and authority

Never gonna happen, and I think you might be stretching anarchist theory. There are too many people on this planet to coexist without organizational hierarchy and authority. You need hierarchy to accomplish any complex task, you need authority to keep some asshole from dumping waste in the river. The point of anarchy, as I understand it, is to make those hierarchies as flat as possible, and those authorities democratically controlled and revokable.

it makes no sense from an anarchist perspective to support a "socialist" state as part of the transition to anarchy. I.e., we should not build systems that we will have to revolt against in the future

There is no future where you don't have to fight some system. Whatever happens between now and the future, there will be a system of some sort. A distributed democratic state with worker-owned industry is probably the easiest system for an anarchist to fight.

Don't get me wrong, each step is going to have challenges, but my goal is to find the path where each transition is as easy as possible. There are still a few steps between market socialism and anarcho-communism. But from my calculations, the next step which is the easiest to transition to and easiest to transition out of is market socialism.

I yell on Lemmy all the time about how the current bourgeoisie are some of the worst creatures ever born, and I am constantly watching news and reading about the vile things the bourgeoisie are capable of

Yeah, it really really sucks to be ahead of the curve on consciousness. But the thing about societal organization is that it requires you to organize society, which takes generations. Society steers like a cruise ship, not a speedboat. If you're going to become politically invested, you're going to have to come to terms with social inertia and develop the patience to slowly usher in an age you'll probably never see come to fruition.