To me, a "schedule" implies intent, not a promise. (Just like a "budget".) There always exist factors out of your control that can blow them, and everyone hopefully is cognizant of that fact.
Thinking that a schedule or budget is ironclad is the same thing as thinking you can predict the future.
The intent is important because it becomes the lid on the project. Without it, it is far harder to stay on track and make meaningful progress in finite time. In a good company everyone involved knows the risks that may make the schedule and budget slip and acts accordingly. Done right, the pressure does not rise unduly shortly before a milestone. It should rise earlier, but also to a much lower level. And a good manager will know when enough is enough and move the deadline before it becomes too stressful.
Good point. Sometimes (often?) though the schedule is taken very seriously as a prediction of the future. The business case for the product is made because it will be ready for the holiday season, or such and such important trade show or whatever. Key people schedule vacations, transfers etc. and are unavailable to help finish the product once reality emerges from optimism.
Thinking that a schedule or budget is ironclad is the same thing as thinking you can predict the future.