Regarding the king's advice, you have to take into account that Rimuru's idea of a leader is that of a democratic one like a president, who is supposed to be subservient to the will of the people and should be humble. Not to mention that japanese society promotes politeness and humility to extreme levels.
Meanwhile, Gazelle's idea of a leader is that of an absolute one, who answers to no one (or in some cases to some sort of deity) and needs to be seen as strong and matchless, since otherwise he risks being betrayed by his own subjects. Not to mention that this world clearly holds a "might makes right" mentality, where people mostly bow to the strong.
So it's not like his advice was that bad, it fits the logic of that world. It's just that Rimuru's style of leadership is completely different and it works for the kind of society he seeks to create. He also has no reason to fear betrayal since his subordinates chose to follow him and he is extremely powerful anyway.
It's also worth mentioning that the story itself points out that Gazielle's style of leadership has left him feeling isolated since the constant need to put up a strong front means he can't form meaningful relationships with pretty much anyone.