I have personally done a few written cases, and have coached people who did it.
Yes, there are definitely more companies using written cases now compared with a few years ago. However, only several companies (e.g. BCG, AT Kearney) are using this new format, and even within these companies, written case adoption varies across offices. For example, BCG does written case in some of its offices but not others.
It is hard to say how this trend will evolve in the next few years, but my guess is that it will continue to spread, but at a pretty slow pace.