I wonder if the problem isn't how to measure productivity, but the fact that we bother to focus on individual contribution rather than how the organization operates with respect to organizational goals.
I work for a mid-sized university. We're a bit unique, for higher ed, in that we have centralized IT. Our projects support university 5-year plans. When projects do not complete successfully or are extraordinarily late people notice. If teams are hitting their goals - university goals - does it matter if every person on a team is hitting some averaged-out metric for productivity? If a team isn't hitting its goals, usually it's not due to individual contribution, it's due to poor communication, unrealistic goals, frequently shifting requirements/priorities, etc. Usually a sit down with the team to get feedback will tell more of why the team failed.
A hobby of mine is coaching youth basketball. To increase my ability, I joined a forum. Today the moderator posted a quote from NBA player Marc Gasol. Marc lamented the tracking of individual stats because the stats don't tell the story. He stated, correctly IMO, that many critical factors are not tracked and would be hard to measure the importance of. For instance, a player who doesn't score much but prevents his defensive assignment from being a play maker (play makers are more than just scorers). Or the player who sets up the plays that allow other people to score (for those familiar with basketball, think screens/picks). Or the guy who is on the bench but helps calm down players when their team is down.
I've come to feel the same way about IT teams. A win is a team win; a loss is a team loss. In both situations, many factors came into play in order for the outcome to occur. My experience is that individual productivity stats don't give you a clear idea why the outcome occurred. In the end, it's all about the success of the organization.