Schedules do not help deliver on time
Schedules do not help deliver a project on time. If they did, no project would ever be late because there are many people who are very, very good at making schedules.
Schedules are measuring tools, like budgets: they help you compare where you are with where you should be. They do not prevent or solve problems.
A schedule doesn't prevent slippage any more than a budget prevents overspending. In both cases it is human behaviour that makes the difference between hit and miss and it is much more efficient to spend your bandwidth (time, money, energy, morale) in nurturing a self-sufficient team where people are engaged and accountable to each other than to create, update and discuss schedules.
Thinking that a schedule will help with delivery is deeply ingrained in some managers who feel vulnerable without one, like a child without their security blanket. It's a big step to let go of the handrail that you thought was holding you up, but it's worth trying.
I'm not saying that you shouldn't prepare schedules, but you shouldn't think that they will help with delivery. Schedules measure progress. People make a project finish on time.