Why is the brand style guide important? Think of your brand identity as your company's personality. It's how the world recognizes you and begins to trust you. If you see someone change how they look and act all the time, you won't feel like you know who they are, and you certainly wouldn't trust them. Imagine a coworker always wears a dress shirt tucked into slacks, with his hair cut neatly short. Now imagine if that same person walked into work one day unshaven, wearing cutoff jeans and sporting a new tattoo of a tiger riding a motorcycle through flames.
It would probably feel uncomfortable because it's not what you used to. You might even check in with him to make sure everything was okay. The same logic applies to branding, inconsistency will confuse and alienate your customers. a style guide is important because it helps your business communicate in a consistent way across all teams and channels.