Over my years in the advertising and marketing world I've heard plenty of good reasons for really getting to know your client's business.
In my experience, there is one great reason for designers, and account teams in particular, to really immerse themselves in their client's brand - it saves time!
When you speak your client's language, understand their values, their mission, who their target consumer is and what their target customer wants, it will save you hours upon hours. How you ask? Primarily, time saved on revisions and back and forth emails.
By knowing your client this well, you are more likely to use the correct messaging, verbiage and imagery right from the get-go. You will know to add the disclaimer that goes on all their print work, even if it has been left out of the copy deck for some reason or that their sponsor's logo always goes on the bottom left-hand corner.
While working on ads for one of the biggest clients I've worked with in my career, I knew which copyright line, phone number, url, logos and disclaimers needed to go on which ad without even having to ask the client. This not only saved us time in rounds of revisions, but it also made our client see that we could be trusted, that we cared and that we paid attention to the details. On several occasions the client thanked us for "catching that". It helped to develop a great relationship with them.
Secondly, it helps save time because if something doesn't quite make sense you know to ask questions up front, before you get started on any work. For instance, if you know your client's consumers well enough to know what they want and need, and the client wants to run a promotion that you think will not speak to their audience, it will be helpful for both you and your client to address your concerns before getting to work so that time is not wasted.
My advice to everyone in the marketing world out there is simple. Become a student of your client's brand. If they're a retailer or eCommerce company, shop at their store or on their website. Use their products and ask questions that you think their customers may have. If it's possible to spend a day at their offices or go through employee training, do so. It's amazing what you'll learn just by seeing how their company operates and what language they use on a day-to-day basis. Read their mission statement and company history. Find out what their value system is and don't forget to study their competition. Knowing what competitors are doing is just as valuable to your client as you knowing what they are doing.