I'm certain Uber is going to start fingerprinting some of their drivers anyway, but for different reason. Parents are now using Uber to shuttle their kids around to/from school and afterschool activities [1]. It's technically not allowed (driving minors/accepting rides for other people) and the UX is not clear but there's real demand for a service like this. There are some recent startups like Shuddle [1] and HopSkipDrive [2] that do this but there's no way Uber is going to sit around and let them eat the market. These startups fingerprint their drivers, so I expect Uber will do the same. With the amount of resources Uber has I wouldn't be surprised if they launched this before the end of this year.
Sources:
[1] Uber Is the New Family Chauffeur http://www.wsj.com/articles/when-uber-is-the-family-chauffeu...
[2] 'Uber For Kids' Service Shuddle Jumps Into Carpooling http://www.forbes.com/sites/ellenhuet/2015/08/24/uber-for-ki...
[3] HopSkipDrive, The Uber For Kids, Picks Up $3.9 Million In Seed Funding http://techcrunch.com/2015/07/14/hopskipdrive-the-uber-for-k...