Is Facebook bad for productivity? Who cares?

I've never understood the management style that is concerned about employees making personal phone calls, sending a personal email, reading the news online, or using social media at work. Even if we don't consider the evidence that using social media at work could improve
productivity (http://socialtimes.com/facebook-is-good-for-productivity-at-work_b120476), from a management standpoint I think there's still a good argument to be made.

Which employee would you rather have?
Jimbob always has Facebook open on his computer. He watches his Twitter feed and Tweets pretty consistently throughout the day. You've seen him send countless text messages and you know he receives personal email on his work email account. He is also one of the top performers in his department when you look at his work outcomes.

Bobbysue doesn't have any social media accounts and hasn't quite mastered the art of text messaging yet. She is consistently annoyed that she sees Jimbob texting at work - she thinks that is inappropriate behavior. Bobbysue struggles to produce work output that is of acceptable quality. She also seems to spend a large amount of time staring down her computer like she's trying to will it to do what she wants. She calls tech support almost daily for what they describe as PEBKAC errors (Problem Exists Between Keyboard and Chair).

From a pure management standpoint, who is the better choice? Sure, these are extreme cases, but the bottom line is - why don't we start managing for output instead of trying to manage how the input happens?