We struggle quite a bit with the mentality that false deadlines create. A lot of end up relying on deadlines to create a senae of urgency, but then important things without deadlines don't get priority and a culture of rushes work reduces the quality of work and work environment.
From Constraints only work if they hurt – Signal v. Noise:
Deadlines are just excuses for death marches (fixed scope, fixed time). Screw deadlines.
Budgets, on the other hand, instruct us to keep quality high but scope variable.
Interesting idea. Budgets have built in deadlines but still give everyone flexibility to focus on important (not urgent) work and work in a better creative environment.