First, gofmt can do more than code formatting, such as applying simplifying code transformations that are semantically equivalent. Second, code formatting and design patterns are indeed related, because the way code is laid out in text is the way that design patterns are expressed. The layout of code affects how abstractions are presented, which affects which abstractions are easy to reason about and work with.
Finally, I picked gofmt because it's a pretty uncontroversial tool, and one that is so successful that even languages like Rust have adopted or are working something similar. I'm really not interested in starting another flamewar about why Go lacks $FEATURE and therefore $OTHER_LANG is better, because we have had enough of those on HN, don't you think?