Some good food for thought. And if you'll permit this accidental essay...
Exaggeration gives characters life.
People who come from a visual character design background may already understand where I’m going with this, but it’s a principle as true in writing as it is in graphic art. We remember the extremes. We notice things which stand out. Without points of exaggeration, any shape is a muddy blob.
Exaggeration doesn’t mean turning everything up to eleven. Like overuse of anything, a character for whom every aspect is exaggerated loops back around to that muddy shape again – no one knows what parts are supposed to be important and they don’t remember the parts you want them to. Proper exaggeration is a choice to focus in on an aspect or two and blow them larger than life. You pick one to three elements of your character's personality and make them shine bright enough that others see them from orbit.
Classic examples of exaggeration are physical ones like extreme height, some prominent feature of the face, or always ending up covered in four layers of mud no matter what situation they’re in. How does this physical exaggeration relate to the concept of a character’s personality? It's something that is always true, and informs how they move through the world on a daily basis. If a character is five feet tall, you can call back to that shortness for everything from not being noticed because they’re below the average eyeline, to constant irritation at being underestimated or belittled, to even their mundane struggles like needing help to reach the top shelf. Physical exaggeration can both lean into a character’s given personality traits (this character is prone to rage, therefore they will be a huge green monster) or deliberately contrast them for dramatic or humorous effect (this character is huge and imposing, but kind and soft as a kitten).
Okay, but what about those exaggerated personality traits? Well, this one’s a little trickier because it relies on solid and confident writing, but also because it’s so variable. There’s as many ways to depict ‘exaggerated intelligence’ as there are writers. Specificity is always good, though. "Highly logical" reads differently than just "Smart". A logical character might express all their concerns in terms of the most pragmatic choice. Their speech direct and clipped rather than flowery. This character always wears practical clothing, their room is sparse and organised, and they stand at attention even in casual conversation. They don’t drink alcohol because it clouds their judgement and impedes decision making. When other people describe them, they should think of them as always acting 'logical'.
You want to exaggerate it further for comedy? Even when this "logical" character is injured or thrown off a cliff, they always have that same stoic expression, stock-still pose, and a near-emotionless response of ‘this situation is not ideal.’ You could play it all up for drama too, if you leaned into their struggle to deeply connect with others, perhaps living a tragic private life full of failed relationships and unfulfilling corporate ladder-climbing as they often appraise others purely by their practical value. This kind of thing could be informed by backstory, but it could just as easily be an element of who they are when everything else is taken away. And it makes even subtle development even more noticeable by contrast.
A lot of people second guess exaggerated traits and smooth them over out of embarrassment or concern that they might be too extreme, and so the personality ends up feeling flat. I often find that I have a strong idea of a character in my head, but once they start interacting with other people I unconsciously pull my punches to avoid being too ‘out there’. Sometimes this is smart and respectful - you don't want to do something disruptive or annoying, and exaggeration shouldn't be an excuse to indulge poor behaviour - but often it’s a kind of anxiety.
The thing is, good exaggeration relies on allowing yourself to be vulnerable once in a while. To look silly, to have a known character trait exploited or challenged, or to cause problems for oneself, and sometimes be a little unsubtle. Pointed exaggeration, by some strange paradox, adds depth of character.
In brief, the purpose of exaggeration is to create a kind of mnemonic outline of your character. It is how one constructs the tip of the iceberg that people will remember and be able to use as a basis for all future understanding of whatever depths they might experience. The intention is to create a character who one can basically understand and enjoy after a single, brief encounter.