So, in response to the "will the ENTIRE online business move" question, the answer is a resounding NO.
The move to mobile will be directly related to how well the various players integrate the user experience and how well they understand where the user is when they are accessing their information via a mobile device. In the travel industry, the early move to mobile was done very badly, simply transitioning websites to a smaller screen without regard to how the user would respond to so many navigation points on such a small screen.
There will always be times that picking up a phone or sitting in front of a professional will make sense and there will be times when the size of the screen will make detailed research much easier on a PC than on the small screen.
Consumers are multi-dimensional and multi-faceted. Your marketing and distribution strategy should be as well.