In my opinion, writing things down helps to clarify your thinking and lets others understand how you think. It also reduces the risk of the devs implementing something that doesn't fix the users' issue.
They think writing things down is overhead, too much "process", too much time. What they (IMO) don't see is that discussing requirements, assumptions before developing a feature (or even prioritizing a feature) helps to establish a common understanding of the issue and the proposed solution.
