My best example was a conversation I had with one of the scientists at my job when she mentioned that she had people spending hours every day generating reports from data our instruments produced. I pointed out that with the code we had it would be simple to generate the reports automatically.
Her response that she had asked repeatedly for a developer to be assigned to the task, but she kept being pushed away because it was low priority.
I couldn't just change the codebase on my own (it was for a medical device), but it was easy enough to spend a lazy afternoon writing a tool to consume the output logs from the device and generate the reports that she needed. That's it: about 4 hours of work and produced something this person had asked for a year prior, and that people were already spending hours each day doing!
The people in charge of vetting requests never even bothered to ask a developer to estimate the task. They just heard that there was a work around, so it immediately became "low priority."