Surely the anarchist would have dismantled the power structure and put some kind of heterarchical system in its place, assuming he had the power to do so. If he was just planning to sit in his special chair and laugh it up, then yes, that is ridiculous.
If one is promoting a system radically different to the status quo, one inevitably has to compromise to some extent to make progress, unless you're planning a violent coup or something.
Would you expect conservatives in 1970s britain to avoid using gas, electricity, trains, the telephone and so on, because they were publicly owned?
Do you expect socialists in modern america not to ever use commercial businesses?