Coaches don't care about chasing stats much at all. They use them as a tool to analyse results, identify tendencies and to help predict likely outcomes. Because that's part of the job of winning.
Fans think stats are an end in and of themselves, because ESPN and fantasy football has brainwashed you into elevating them beyond the game itself. Fans use stats like some kind of sorry consolation prize when their team is sat at home watching the Super Bowl, posting things like "yeah, but we almost had the most sacks in the NFL, dude". Who really cares? Did George Rogers leading the league in rushing in his rookie year make us any better than a 4-12 team? No, it didn't.