2 wrongs does not make a right and the act of vengeance is not the equivalent of learning from mistakes.

Preventing mistakes, maybe.

No person who is hell bent on doing revenge has ever made a success out of themselves. (e.g N. Korea)

Probably not true. Plus, your example is horrible. North Korea is an independent country that is not struggling. A better example would be the Nazis, or the USSR where they actually have gone away.

The first step of spiritual success is to forgive, but not to forget.

Holding a grudge just has a little less forgiveness, so close to spiritual success.

And all philosophers agree that wrath is a useless emotion.

Philosophers only get to exist in society. A philosopher in an uncivilized world is known as useless. Maybe revenge helped in those times.

I'm not dismissing them at all, just stating that they aren't necessarily relevant to the question "What is the use of anger?" and pointing out that traits don't necessarily have to have a legitimate function.

Don't forget that what I have linked is not a hypothesis, but a theory. A link further down goes to the actual study, as well as predictions made and verified by said theory. That doesn't necessarily make it correct, but it makes it the best fit we currently have.

1) Violence is necessitated in nearly all species at a base level as part of competition for resources. Among other things, anger and violence can be leveraged in a dispute over potential mates. Violence may damage a bargain with one individual, but prior to such things as the Better Business Bureau there was little stopping someone from just bargaining with someone else.

2) It's not a direct cause-effect relationship. It's more like this: Anger -> Better bargaining position -> More available resources and mates as well as better chance to survive. It doesn't make them a better fit for reproduction, it makes them more likely to survive long enough to reproduce, and with additional resources makes it more likely for them to reproduce more, and more likely for the resultant offspring to survive to sexual maturity and reproduce themselves. Genetic success is a numbers game, and there are many ways to either succeed or fail, as can be seen in the diversity of life in general and the varying reproductive practices of different species. I might also suggest that mistrust and fear mattered little to the reproductive success of an individual in times before there was any kind of legal structure (or even a word for rape).

3) Positive reinforcement is a relatively new concept all told; it's not something we typically see in the wild- at least not in and of itself. Furthermore, a combination of positive reinforcement and discipline is more effective than either alone.

I'll acknowledge that in modern society, anger makes little sense; but early man did not have any of the advantages that we now take for granted; the benefits of anger are greatly amplified in such a circumstance, and the drawbacks (which ultimately take the form of increased risk of death) are somewhat mitigated by a significantly lower life expectancy anyway.

I should also reiterate that the theory I've posted does in fact make sense, back up it's claim, and can make valid demonstrable predictions using its conclusion as a premise. Are you suggesting that you can offer a data point that puts that conclusion under dispute? If so, I'd like to see it; otherwise I'm going to stick with the accepted theory until the data doesn't pan out, and then see how it can be revised.