TL;DR Stack Overflow is modeled after real world free market economy. All which is described is perfectly normal as it is.
In economic terms, something like this is happening:
We have one huge abstract market - this is Stack Overflow itself. There are lots and lots of questions being asked and answered. Demand meets supply and all that. There is also reputation involved. In a way reputation count is similar to money in real world. It is being acquired by supplying the demand. You can also exchange it for services - pay some rep to see your question answered faster and better (or at all). That number also gives you a higher ranking on a list and greater privileges in the community - yup, pretty much like money in real world.
But wait, not everything seems to be quite right! Following the same analogy we notice that in real world different services cost different amount of money. On Stack Overflow every upvote on a post gives you same amount of rep, regardless of how hard the question is. So, an answer How do I sum an array of numbers in Java? is in theory equally worth as question How do I write a monadic IO wrapper in Haskell?
Parameters which do influence how much rep you'll get are question's visibility, i.e. how many views did it attract, speed of delivering the answer and its relative quality compared to other answers. I'd argue that for the 'low hanging fruit' questions we are talking about now, visibility and speed are the most influential parameters, but I don't have any data to back that claim.
So, basically the general community values speed of delivery and services wanted by many over detailed quality and obscure services wanted by a tiny minority. Except the speed part, this is a tautology - the majority values what majority wants. This is also a feature of real world economy. You can get a lot more money if you produce a cheap product with few features and sell it to many, than if you hand craft it out of mahogany wood, pack it in cloth woven by Tibetan monks and sell it to the few who need it. This is a natural consequence of the initial premise and the fact that the unit price of one upvote is the same for all questions doesn't make much of a difference.
Also, another example of how Stack Overflow is different from a real world market-driven economy is that here demand also gets currency just because it exists, i.e. upvotes on questions also give us reputation points. However, this difference is also superficial. Most modern economies use some means to 'motivate' the consumption of produced goods and services in order to avoid what is known as overproduction crisis. Details are different but shortly consumers are being rewarded for consuming rather than abstain from consumption - subsidies in real world, rep gained from asking a question over here. One notable difference on Stack Overflow is that you can get a very large reputation score by asking a very large number of questions. However, this affects a number of users which is too small to make a significant difference.
Now, there is one particular thing that attracted my attention and I formulated a theory: Someone posts a trivially easy question. In a matter of seconds there are several answers already. The question may be of very low quality it may be even a duplicate, but nobody cares. Why should they if it means easy rep. What happens next is that each answerer upvotes a few of the competing questions hoping that others would do the same and he will get some rep for that answer. Very often it is so and rep farming continues. So, the key ingredient of this exploit is neither visibility nor relative quality of answer. It's cooperation between answerers. Unspoken rule to upvote a few competing answers hoping that they will do the same. Low quality questions are just a resource for this process. A blank field where these users can vote for each other. In SEO world this is known as a link farm or Google bomb. For sake of consistency, I'll name one economic analogy here too - a bubble. And one thing we know about bubbles is that eventually they break (or pop, which would be more idiomatic to English?). So, once in a while someone loses a huge amount of rep after recalc because many of the questions he answered were closed. And if that doesn't happen and many users keep gaining huge amounts of reputation points there is something else behind the corner:
Inflation: If everyone has more than 10k rep points then nobody really does. At this point (we are not there yet but we may or may not reach that state) reputation won't matter at all. If people make a judgement about your expertise mostly by looking at your reputation score now (and that would be stupid) they wouldn't even look at it then. They would instead look for your tag-specific scores, some specific badges and most importantly a sample of your post, which they should be doing now already. When there is no more valuable money, only goods itself are what matters.
And after this wall of text, to finally answer your actual question:
Does Stack Overflow need another incentive to make users answer questions?
No. There are quite enough incentives as it is. You focused on the most obvious ones like reputation and badges, but there are others much more For example, my own incentive for writing all this wasn't that I will maybe get some reputation points or a badge. Writing all of this just to formulate a theory was almost a reward for itself. Also, there is that sadistic pleasure in knowing that someone will surely read all the way down here.