Co-ops still have boards and often employees that report to the board (or another employee). There's a structure there, but they also tend to be smaller so the structure has less impact.

I was treasurer of my housing co-op and we had one full-time employee who reported to me and the board. That employee (the coordinator) hired contractors for maintenance, bookkeeping, as well as things like the laundry machines.

Even large co-ops (like clothing stores) have the members vote a board in that sets up the structure.