Making a site look and feel consistent across the board is absolutely key. If a customer is looking at our site and we have different colours and styles for each button, link or body of text then we're going to confuse them.
By keeping different elements unique, but branded means people won't get confused as easily. A customer should be able to tell from looking at an element (be it a button, navigation menu or copy) what that is and how much attention they should pay.
Users these days know that coloured or underlined text usually means they can click on it. By keeping this type of styling uniform we can help customers understand the site.