You can already use Facebook for free on mobile. I don't think FB has big interest in providing free internet for everyone.
(a) having a competitive advantage in raw, large-scaled _metrics_ that Google does not have (see also: Facebook's emotion and behavioral studies[0])
(b) Being able to monetize their advertising platform better. They are well aware that their current numbers are blown up by fake likes, and clickfarms [1]
At least this is just my take. I'm sure there are also other interests behind the scenes.
[0]: http://www.nytimes.com/2014/06/30/technology/facebook-tinker...