Tropes and Cliches

Stoic Characters

So there are stoic characters in just about every fantasy anime, or game I've watched/ played. In Akame ga Kill, it was the title character, Akame. In the Assassin's Creed series there's Connor Kenway aka Ratonhnhaké:ton.  Varies members of Organization XIII in the Kingdom Hearts series. This list goes on. Now there are a number of reasons on why these characters are like this, and people tend to ignore those reasons. It can be anywhere from PTSD or other mental/neurological reasons to the moment they lose their shit everyone will fall apart and we don't need that. Now I'll be using two of the examples from above and then other examples because there are many ways to write these characters. Plus people often confuse this as being emotionless/ cold hearted which is often not the case. 
So being stoic is being calm and almost without any emotion. When you're stoic, you don't show what you're feeling and you also accept whatever is happening( though that may not always be the case). The noun stoic is a person who's not very emotional. The adjective stoic describes any person, action, or thing that seems emotionless and almost blank..So basically their face is the equivalent to a Botox injection. They can be Heroes, antagonists or anti-heroes. On The Team they will contrast the Hot-Blooded. 
Also Spoilers....
Starting with Akame Ga Kill, Akame was trained as an assassin and still kick so much ass after she left and joined NightRaid. At first she does in fact seemed cold and distant, but there is a reason behind it. Akame was infamously known for being the Empire's number one assassin. Akame's cold-hearted and serious demeanor stems from her hellish training the Empire forced her and her sister through after being sold by their parents. She was trained to suppress her emotions and keep them in check at all times. Plus she is known to crack a smile every now and then. But the moment she did show emotion was when Sheele died, she broke down crying. So she was basically using her training as an assassin of the Empire to stop herself from loosing her shit
Moving on the Ratonhnhaké:ton... well there's a cultural reason behind all of it. But some background info first. Ratonhnhaké:ton is a Native American from what English speakers call the Mohawks. He lost his mother at a young age ( 4) and basically watched her and several others be burned alive because of a man's man crush on his father.He has the bearing of The Stoic and a belief in standing firm against everything life throws at you, but he is also very emotive and highly sensitive depending on the context. This stems from what he was raised around. He was taught not to show emotions around outsiders( not sure why) because it could be exploited as a weakness. He puts on his stoic face around the Patriots, but the moment he returns to the Homestead he actually cracks a smile. He is caring, but was taught not to show it. 

There are more examples and reasons behind it( Most of which are from comic books):

-In X2: X-Men United, Lady Deathstrike barely changes expression or talks which is justified since she was being mind-controlled by Stryker.

-Batman in general, because let's be honest, if  he wasn't like this shit wouldn't get down. Plus I think it's more a psychological tactic to make sure the bad guys don't know they got under his skin.

-Black Panther is very stoic, usually only getting particularly emotive in private or around those close to him. This is a consequence of his tragic upbringing, as he was forced to begin training to become the new king of Wakanda at a very young age after his father was murdered.

-Agent 47 from the Hitman series.

-Various members of Organization XIII(, Xemnas, Xaldin, Lexeaus, Zexion and Saix to name a few) are various shades of stoic, though they all have moments of emotions. This is due to their lack of hearts. 

Hell it was even popular back in ancient Greece. Stoicism, without the deterministic mythology associated with its original forms,  was seen as effective in  both at preventing and treating some forms of depression and anxiety. By teaching the patient that they can always be in control of their own mental state, the patient can use stoic discipline to become resistant to emotional disturbances.The stoics of ancient Greece both were and weren't this trope. They didn't dislike being emotional, it's just that they saw excess emotion as negative because it can control a person's life, leading people to believe that emotions can lead to bad decisions. They believed using logic and reason to determine their life led to greater happiness.

There is nothing wrong with writing a character like this, just give a little backstory on why their like this. Kayden's love for a guy led him to make one bad decision and it resulted in him losing his kingdom. Penny's been traumatized at a young age, that's all we know and she doesn't like talking about. Mack's on the spectrum and expressing certain emotions is difficult.So on and so forth.