Taking away the date is definitely not the right move. Now you've given every PM and sales guy carte blanche to throw whatever flavor-of-the-moment idea comes in their head. The team will be churning constantly to keep up with the requirements and then someone will suggest, "I know, let's do scrum!" so now we can all enjoy the stress of unreasonable deadlines on a continuous rather than waterfall basis.
To the contrary: a properly-managed date is an incredibly valuable constraint which the entire team can use to make tradeoffs against. To make it work management needs to trust the team, and engineers need to understand the larger business picture because they are the ones with the knowledge to find creative solutions that actually work and decrease time to value without compromising technical quality or long-term maintainability.