The Status Quo
Anyone with experience practicing law or dealing with lawyers knows that a significant subset of lawyers are stubborn, difficult to deal with, poor communicators, uncivil, or generally assholes. This isn't too surprising. The educational process for lawyers screens people for verbal and analytical intelligence and a high level of literacy, not for their interpersonal negotiation skills and overall mental health.
Politicians and other leaders also often have very negative personality traits and behavioral patterns that conventional wisdom would assume is ill-suited to cooperating constructively with others to get things accomplished in a manner that doesn't lead to extreme conflicts.
This also isn't too surprising. Politicians are screened mostly for the mass marketing abilities, their ability to raise money from wealthy individuals with strong ideological preferences, and for their loyalty to a set of ideologies that produce the most change possible while securing majority support in a particular geographic area. Playing well with others, building broader than majority coalitions, and overall mental health aren't screened for very rigorously in the hiring process (at least in the U.S. with a relatively open access to candidacy process — parliamentary systems with strong political parties can be another story).
The Primary Question
How viable would it be, however, to create a guild or profession (perhaps they might be called "diplomats" or "ambassadors") that was screened primarily based upon the good mental health and strong interpersonal interaction and negotiation skills of the members, who would then be given responsibility for tasks within the society such as dispute resolution and establishing societal level political compromises?
Some of the things the scope of "good mental health" and "strong interpersonal interaction skills" would include a tendency to pick up the phone and talk things over with someone before taking action, a lack of a tendency to procrastinate, promptness, good emotional control, a strong capacity for empathy, good listening skills, clear communication styles, etc.
The professionals within the guild would receive education enabling them to carry out their various tasks, just as professionals carrying out those tasks do today (i.e. this wouldn't just be a group of people selected for personal traits but not trained in their specific jobs). But, the personal traits would be a prerequisite to entering this training regime, and lots of the evaluation and ranking of people within the guild during the course of their educations, when they were hired to first and later jobs, and as they are evaluated for promotions and prime opportunities down the line, would incentivize being exemplary in these personal traits.
In this society, you would no more put someone without this kind of professional screening in charge of litigation or negotiations or political decision making, than you would put someone without engineering/architecture training in charge of designing a bridge or a skyscraper or an automobile.
General intelligence might be necessary at some level to do guild work, but it would not be the focus of the criteria used to evaluate people in this field, it would only be relevant to the extent that someone was too low in general intelligence to carry out other aspects of the profession in an adequate manner.
Would it be viable to establish screening mechanisms sufficient for the task with behavioral science knowledge only modestly (a decade or two more of progress tops) better than what already exists today? Assume that this society has technology more or less comparable to that of our current world in all other respects.
Would this kind of rigorous character and personality screening really make a difference in how tasks entrusted to this profession were carried out, or is the ugly side of behavior in the professional lives of people like attorneys and politicians mostly a product of the context in which they are placed such that anyone in their shoes would act similarly?
Would a guild established on this basis, once in place, be able to maintain their dominance over this kind of activity, in the face of efforts of other people who are disqualified from guild membership by virtue of their lack of the personal traits necessary to be a guild member? Or, would people ineligible to be guild members successfully steal guild member's business. In particular, would they be able to steal this business because something about the personal traits that would make people like many existing lawyers, politicians, leaders and negotiators ineligible for guild members, has intrinsic positive value that is superior to the collective value created by having a group of people who have undergone guild personal trait screening. In other words, are assholes and ideological nutjobs more effective at their jobs because they are the way they are, than people who have traits that conventional wisdom assumes are better suited for negotiation and cooperation?