Why does it have to only be about productivity? Sure, on a larger scale BYOD should be about productivity, but it is about how you make your employees happy that matters. Productivity increases because of how you treat your employees. Unfortunately, it's not the other way around.
Some employees work better at a remote location. Some employees adapt to their own device. Other employees are just stubborn and feel like company devices are slow and prevent them from doing work in a timely manner. Whatever the excuse may be, BYOD policies can assist in productivity.
It all comes down to keeping your employees happy. Don't look at BYOD policies as a chore, but a way to benefit your employees, as well as your business. Why not use BYOD policies as an incentive?