Obviously, it is true that Kurn was "riding the crew pretty hard" as Geordi & Wesley remarked to Cmdr Riker. Kurn made it clear he viewed the culture as soft, and he was going to be as strict as possible with them, push them even unnecessarily (as with an inspection during an engineering maintenance cycle). He was harassing them to establish dominance. And to test their mettle, perhaps to gain insight into his brother's unique character. (To see if Worf could successfully bring a challenge to the High Council.
Riker may have couched his "suggestion" in polite language, but it
was a challenge to a superior's judgment in an authoritative command structure. On a Klingon ship, top-down "obey or else" must be the more common communication structure. Kurn cut through the niceties to the heart of the rivalry.
He probably even considered Wesley's defiance of his phrasing "execute" a challenge. Picard's subtle nod of acceptability there seemed to say, "Yes, we've all wanted to kill Wesley, but that would be too easy."
IE, the reality is that Kurn may have had to repress the real impulse to answer Riker's lethal challenge. The assumption of killing Riker was just bravado (or underestimation of the adversary).
Also, Kurn
was adapting to their multidirectional feedback structure. There was some humility/team player in him after all.
One issue with Troi is very typical of Hollywood's portrayals of psychologists: they think all shrinks can do is nod, say "and how do you feel about that," state the obvious armchair impression as a diagnosis, play role reversals, and then have personal relationships with their clients.
Troi ought to be doing what the medical staff does during alien encounters:
prepare. Maybe hold an orientation briefing once in a while. Not stand around watching fireworks.