The FAA is indicating that preventing the pet from flying would not solve the issue.
Finding stats on the number of pets carried in the cabin is hard! However i have eventually found something while researching law suits against airlines over pet allergies (none have been successful that I can find).
This article makes reference that Air Canada changes its ‘pet in cabin’ policy on 2009, apparently in response to Westjet already allowing it. The reported stat is that westjet carried pets in cabin on 25% of its flights!
Pets in airplane cabins: an unnecessary allergic hazard