There is something interesting in the idea of larger ranges. Currently there is the very narrow (1 point) and the very broad (ability benchmarks like 1k, 2k, 10k). Using levels rather than points causes people to think more generally about their behavior. It might cause an increase in focus on "things that matter" rather than points.
Then again, the point system, properly designed is supposed to make points reflect things that matter. Caring about whether or not your answer will get voted up typically equates to writing a good answer. Since the points are aligned with broader site goals, there is little harm to showing the exact score.
One possible caveat is that users are focusing on the score, and on writing good questions, but somehow ignoring "other" aspects, perhaps the types of things that cannot be quantified, like, "being nice" or "welcoming new users". I consider this a quantitative bias which typically occurs whenever some concrete metric is introduced. The analogy to grading in schools might be that if teachers relaxed grading schemes, then students would question deep truths and seek great insight if they weren't chasing to hit 89.5 on their next exam. Then again, if teachers didn't give grades, students might not show up.
The SO solution has been to simply point-ify or badge-ify everything, closing any leaks in the extrinsic motivation vessel wherever they appear. It doesn't seem like your proposal would fit into that so well, since suddenly points wouldn't matter immediately. Instant feedback is one of the hallmarks of user-interface and game design; psychologists have long known that the proximity between a reward and a behavior is highly correlated with the reward's effectiveness at conditioning the behavior. In other words, the rat won't push the button if the cocaine only comes out two weeks after the push.
In sum, there's always a temptation to relax or do away with overly specific schemes of extrinsic motivation. Yet, since SO was designed to capture coders and gamers, two communities which live and die by 'the detail', a broader-ranged reputation probably wouldn't satisfy their carnal thirst for numeric validation. I was a philosophy/polisci major, so I don't value anything not amenable to Hegelian synthesis. We all have our tendencies.