A problem is that karma attempts to capture orthogonal values in a single number. Even though you can reduce those values to a single number they still need to be captured as separate values e.g. slashdot karma system for a half-assed example.
Karma seems to roughly fall into one of three buckets. The first is entertainment value e.g. a particularly witty comment that nonetheless does not add material value to the discussion. The second is informational value e.g. posting a link to particularly relevant literature of which many people are unaware. The third is argumentative value e.g. a well-reasoned and interesting perspective. All of these are captured as "karma" to some extent or another.
Objections are that this makes it difficult to filter content based on karma, which raises questions about its value. If, for example, I am primarily interested in reading hilarious witticism and interesting layman opinions, there is no way to filter out comments that contain dry references to academic literature. Alternatively, if I lack an appropriate sense of humor I might find the karma attributed to immaterial witticism inexplicable.
Even if a clever system was devised and ease of use was ignored, there are still issues of gaming and perverse incentives (e.g. Gibbard-Satterthwaite theorem et al). To misappropriate an old saying, "karma is a bitch".
I can think of at least 2 kinds of value you missed:
Artistic value, for things like well written stories and non-humorus but inspirational images made.
Implied effort values, for things like summaries that required reading through some huge number of articles but isn't that impressive itself other than letting people know that those hundreds of articles didn't contain anything interesting and saving them the trouble to read them.
I consider this a low value post, because it muses about a particular idea without actually doing hard work to get it done. (I do not have the knowledge or resources to do so, or even know if it's possible to implement this idea on Less Wrong. I'm not even sure if it would be worth the effort)
There are posts that I upvote because I thought they were funny, mildly informative or well reasoned. Sometimes I upvote a simple (easy to produce) link to a good article. Sometimes I admit I upvote them simply because I agree with them (I generally don't upvote things I agree with if they use bad reasoning, but I am less likely to upvote something I DON'T agree with unless it is extremely well thought out, to the point that I actually updated my beliefs because of it.) I don't apologize for that - it's a natural outgrowth of the Karma system. It costs me nothing to give Karma to whatever I like and there is no means to enforce any particular usage of Karma.
But there are things I upvote because they were actually important and good and required hard work to put together. And I feel a little bit sad that the most I can reward those things is with a "click" that is exactly as valuable as the click I give people who said something mildly funny.
High value posts tend to acquire a lot of Karma because a lot of people feel motivated to click. But I think there is a qualitative difference between a guy who makes one amazing post that gathers 80 Karma and a guy who makes 80 posts that are kinda neat. I think it would interesting, fun, and potentially valuable to distinguish between those kinds of people.
So what if we had regular Karma, and then we had some kind of Superkarma. (Perhaps a good name would be "Status"). Status points would be genuinely rare - when you give one, you are not allowed to give another one for at least 24 hours. You can still give them to a funny joke or viewpoint that aligns with your tribe, but I think assigning them rarity would encourage people to reward genuinely important things. (I'm not sure 24 hours is the ideal waiting period, it just sounded nice).
I'm actually kinda amazed by how much I care about Karma. I get a "sweet, level up!" message in my head every time I see that I've passed another 100 points. But most of my Karma is from random comments. The two fastest upvoted posts I made were links to an article about the Singularity and a webcomic, neither of which required much effort on my part. The fact that my more serious posts are judged by the same metric is (slightly) demotivating.