I was listening to this podcast: https://soundcloud.com/whatisleftpod/unlocked-planet-of-co-ops
It has some really interesting things to say about the downsides of direct-democracy (although I warn you that the speakers do seem rather self-congratulatory and sort of "wind each other up" over the course of the podcast. It's definitely an interesting listen through.)
The relevant passage starts at about 28 minutes in.
The substance of the critique appears to be something along the lines of: direct democracies are ruled by informal cliques, demagogic charismatic speakers, etc. At least with hierarchical structures, you know who your boss is, and where the power is. In direct-democratic structures, there are still hierarchies, but they are invisible. (They don't seem to consider the possibility that these "invisible" or "illegible" hierarchies are also present in formally hierarchical organisations, or at least they seem to think that the visible hierarchy compensates or mitigates against this somehow).
I think probably a lot of you will agree with the assessment of "cooperatives within capitalism / the market", but I would be interested to see what people had to say about the critique of direct democracy specifically, since if the argument is correct then it cuts to the core of a lot of anarchist / libcom thought.