I’m currently part of a cooperative/non-hierarchical team. We have a program manager but no technical leads. On a very busy and essentially leaderless team like ours, you can’t just throw an essential task out and hope someone will pick it up and get it done before the deadline.
We follow an agile process and adding a task to the backlog and getting it assigned and done the usual way works fine for much of our work, but not so well for tasks that seem like red tape, are unpleasant, or are outside normal development work. With this team dynamic, when you need something important done, it’s best to assign it to a specific team member and give them the option to suggest someone else if they don’t think they’re the best person to work the task.