As a manager it's my duty to create a safe space and frame the challenge in a manner that doesn't create friction in the team. When an engineer says it takes 4 weeks I well and truly trust them, all that I seek is
why. Because whey they then get down to one or two level deeper details they typically uncover more unknowns and for all you know it may in fact end up as 6 weeks.
Also, none of this happens on the spot; as in "tell me right know why it takes 4 weeks, let's do a 30 mins white board session". Having been an engineer I totally understand interruptions and, as a manager, interrupting my team is like shooting myself in the foot. When I say "conversation" it happens asynchronously over several days. I encourage them to spend a day or half a day to work out task break downs and dependencies because it takes a different frame of mind to "plan" a task as opposed to "working" on them.
> Are you truly going to lose customers, or are you just trying to pressure people in "being accurate",
It's a combination of both though I wouldn't phrase the latter as "pressure" or "being accurate". It's a way to discover information that will increase my team's confidence in delivering the project. As we all know most of the project failures are not because people slack but because they uncover a dependency too late down the line or they don't validate an assumption or a new constraint is discovered. Most of which could be accounted for with a simple planning process.
I do recognise though that most engineers don't like planning or task breakdown and so I spend quite a bit of time to take much of the heavy lifting so that they don't spend more than 10% of their time on it. As a manager I am held accountable for my team's delivery and I absolutely want engineers to be spending most of their time on writing/delivering software. One example is I don't ask for plans/task-breakdowns for anything less than a week. In fact there's not even a debate; on the contrary if an engineer says 3 days I ask them to round it up to 5 days (a week). Only for tasks that are longer than a week I may get into the details and for more than 2 weeks it's almost mandatory.
> developers say things to get managers out of their hair
This seems like a well and truly dysfunctional team. Engineers and managers are partners and only when they work together can they deliver something meaningful. I would address this mis-trust or friction first because if there's no transparency within a team then all bets are off. We'll end up with a series of failed projects, burnt out engineers, operational nightmare and what not. What I've noticed is these social frictions end up manifesting as "estimation problems" and people try to address the symptom by trying out different project management processes each of which fail spectacularly.