It's also tough to be that honest at some organizations.

Like if your manager said, I'm trying to reduce our costs by 10% so that I can get a big incentive bonus personally...

Don't really see why motive matters in that case. The idea of misstating the problem doesn't exist (the bonus and the cost reductions are intrinsically tied to one another) and the additional clarity doesn't guarantee the desired behavior. It's possible a subordinate might not help you if they don't feel your personal gain is beneficial to them.

If a manager says "I need to reduce costs by 10%", the specific desired business outcome is clear. Reminding your subordinates that your pay and continued employment is tied to you completely the tasks and requests of the people you answer to doesn't seem needed. This isn't about "some organizations", it's just about efficiency.

Organizations always want to reduce costs, there is always pressure to be efficient and reduce costs.

Usually the current costs are the cost of business, and if there is an externality ie economic downturn, some crisis, big lost deals, then there may be renewed pressure at which point this has already been communicated by the leadership to the org and everyone is on the same page.

Trying to reduce costs out of the blue is not usual, it suggests some individual thinks there is some inefficiency after studying the issue, or its a management consultant recently hired to explore that, but usually the people being requested for information would be briefed and know exactly the reason and why.

That's eventually how it worked out, but time and money were wasted in the process. Lots of man hours invested into justifying existing costs/orgs/projects.

When I could have offered up lower lying fruit if exact cost was identified as the driver up front. The questions weren't easy to translate into actual intent at first. Leadership styles profoundly affect efficiency.