That said, I agree with your criticism of communism / anarcho-syndacalism: if you remove capitalism, you are moving power into party politics, which creates even greater inequality to what we have today and explains the horror of communism we've seen in the past century.
They most certainly are not. Some right-libertarians have convinced themselves that they are anarchists so that they can pretend to be radicals but that does not make it so. Anarchism and capitalism are incompatible, anarchism is a left-wing ideology that among other things, seeks the end of capitalism.
I don't know why you interpreted my comment as being a criticism of communism or anarcho-syndicalism (it was just a probing question to understand what somebody thought anarchism would look like), and neither does your criticism of those ideologies make much sense. I don't think you actually know what anarcho-syndicalism is if you think it involves party politics.
That said, I agree with your criticism of communism / anarcho-syndacalism: if you remove capitalism, you are moving power into party politics, which creates even greater inequality to what we have today and explains the horror of communism we've seen in the past century.