My department has a positive culture, which can be a problem. I want to hear some negativity from my team.
That's counter-intuitive, because we got to be leaders by having a positive attitude, and we want our people to be positive. That's in line with current leadership culture, which allows little place for negative thinking.
That approach is based on a false premise, which is that things are always good. Truth is, some ideas are bad and some actions are ineffective and some people don't care, so unrelenting positivity is a result of either self-delusion or good meds.
Your team has a lot of negative thoughts. If your culture doesn't encourage them to lay their doubts on the table, you miss the opportunity to help them see the whole picture. Or maybe you miss an early warning that there's trouble ahead. Bottom line: If they're not with you, you want to know early on.
Don't fool yourself: If they're thinking it, they're saying it. If they don't say it to you or the group, they'll vent in the lunch room or at the water cooler. That's the kind of negativity we all fear, because it de-motivates.
Healthy skepticism, expressed in terms of actions and outcomes ("I think if we do this, the outcome will be this bad thing") is a critical part of developing good plans and processes. Not everyone is articulate, though, so what you're likely to hear is what we all hate: "That won't work."
When you hear that, probe. Find out why they think it won't work, and ask what they think would. It could save you a lot of heart-ache later on.
You hear a lot of grousing from the most can-do people in the most motivated and capable organizations in the world: elite military units. They bitch because they have high standards and high expectations, and they won't settle. That's what you want in your team.