So long as we include electronic communications in the category of “written communication” written communication is very much in favor in today’s business context.
Today, communicating in writing is much easier than it was in the past. In the past, memoranda in offices had to be created through a fairly involved process. A person wanting to send a memo would have to call a stenographer who would take down the message as the person dictated it. The stenographer would then go and type the memo and bring it back to be signed. This took time and a good deal of labor. Today, that process is much faster and easier. The person who wants to send a memo needs only type it on their computer and send it via email to whoever needs to get it.
In addition, written communication is stored much more easily today. Businesses no longer need to keep voluminous files of paper memos. Instead, everything anyone sends as email and every document anyone produces can be easily stored in computer memory.
Today, written communication is much easier to create and much easier to store. Therefore, it is in favor as much as it ever was in the business context. However, if you mean hand-written or type-written communication, this has gone out of favor because of the advantages of various electronic communications.