If you leave open the responsibility to everybody, don’t be surprised of nothing gets done. Everyone is leaning on the other person to take care of it.
Assignments are made to be direct. So are dates, even if they’re just arbitrary. People respond to definiteness and delay on vagueness.
You don’t need an excess of people to accomplish a job. More doesn’t always mean better; more may actually mean less outcome. What you need are clear roles and responsibilities.
Dish out exactly what you expect in return. “Just do it” sometimes creates an excuse to just slack off.