It cuts both ways. In my experience working in the second environment, where deadlines are arbitrary, managers and leaders do not do the work to decide what is

It cuts both ways. In my experience working in the second environment, where deadlines are arbitrary, managers and leaders do not do the work to decide what is important or what it means to “be done”. You can start out with the prior that deadlines are important and discover that there are activities that may need to be done that will blow your deadline. You can seek clarification on what should be done, but be told either of “don’t tell me the details”, “figure it out”, “I trust you to make the right decision” etc. In environments where deadlines really matter, managers are much more willing to make decisions about scope and control it closely and work with their colleagues to define a done state, because it actually matters.