I've always wanted to see regular anonymous mass surveys of employees, about things like project progress and completion dates.
Do you want to know when a feature will be finished? You can analyze story points and build a fancy burn down chart, or you can just ask the people working on the feature. Allow the entire team to anonymously predict when the feature will be finished and I'll bet you get a better answer.
Anonymity is important because people are easily pressured into changing their answers. We've all been asked "how long do you think this will take?". "Two months" you answer. Then managers pressure you into changing your answer, but usually, no matter what you're forced into saying, you still think it will take two months.
Why did they ask if they didn't want my answer? Therein lies the truth. Companies don't want accurate answers and data, they want to see and hear what makes them happy right now.
I don't think most companies would have the courage to regularly gather data with anonymous surveys.
But maybe, if one clear-headed and high-level executive wanted to force it on the company, they could. They could mandate the use of a software tool to do anonymous surveys, and no matter how much lower-level managers complained, the team could still anonymously say when they actually believe the project will be finished. Etc.