I would argue that showing this information, while interesting, is more likely to lead to false assumptions than just showing the reputation in full aggregate.
For example, some questions / answers get a large number of up-votes because they are funny or ironic or fall into the "interesting discussion" category. (arguably, the later happens much less now, but early on this was a major source of rep for a number of users)
Another way these numbers can get skewed is by the volume of questions, answers, and edits. One user that has only a handful of answers, but has a ton of rep from those few answers is, in my opinion, better at answering than someone who has answered a lot of questions but only gotten a vote or two each. The same goes for questions as well. Raw score doesn't indicate quality necesarily, but instead indicates a combination of quantity and quality.
I do agree that more data regarding a user's contributions would be great to have, but many people, myself included, are not as statistically-aware of what numbers mean. A number that gives the wrong impression or is used poorly is worse than no number at all. Statistics of all kinds wield great power, and with that power comes the responsibility to provide and portray those statistics in as accurate and easily comprehensible way as possible.
The point I am trying to make is that taking an aggregate number and breaking it out by category often changes the meaning, or at least adds another dimension to the meaning of it.
Reputation as it is now indicates the value of a user's participation to the community. By breaking that out into categories, you are not changing the meaning of the number (ie. you can't draw any conclusions about quality of answers or questions), but instead you are showing the value of the user's answers and questions to the community. Quality or knowledge can't be determined any more from the breakdown than it can from the aggregate.