I think you're not really in touch and being honest with yourself if you don't think both aggression and anxiety play a crucial role in your life. Or maybe you just have different definitions of those words than I do.
I've been trying very hard to break out of this cycle and can tell you first hand it's not in anyway beneficial or pleasant and is actually very very destructive.
I see your grandparent may have something I've noticed is a common misconception, not just in the analysis of the value of human traits, but also in the analysis of modules in software, and other engineering projects.
This misconception boils down to believing that just because a trait/emotion/module is not being used for the "reason" it was originally intended (scare quotes to prevent implied creator relationship to evolution) that the trait/emotion/module is unusable, or bad.
That's an interesting viewpoint, usually coming from people who believe that their world is governed by fairness. I'm not sure that's reflected in reality.
Sometimes aggression is constructive or useful in situations like negotiating. Sometimes it is counterproductive and considered harmful.
What I took away from the OP is that we cannot blindly act on our emotions - that having an intermediate, self-reflective and self-questioning step in how we act and think is vital in order to be happy and successful in the world in which we live.
And, of course, this includes questioning the self-questioning. Sometimes it's the wrong time to question, and it is the right time to act on unfettered emotion.
The question is, when? ;)
For instance, rather than worry constantly about impending doom you can just calmly go about preparing for worst case circumstances. Same result -- perhaps a better result -- and far less suffering.
We should all seek to calmly and rationally seek the best interests of ourselves and people around us, without having to be paralyzed by fear, anxiety and other negative emotions.
All motive lies with emotion and feeling. Who gets fat without taste buds?
Heck yes!
Anxiety instills fear in the consequences of bad code being released into the wild.
Aggression allows speaking your mind when others around do not meet the standards you espouse.
Such things remind me all too often of the fix point combinator and what not. But I'm anxious to miss the point, because at some point logical reasoning doesn't work anymore and leads into a trap, e.g. in case of greed.
Hard times create strong men, Strong men create good times, Good times create weak men, Weak men create hard times.
Anxiety makes you consider consequences of your choices and take action based on it. Aggression helps you fight for what you think is important.
Does that mean they're useful in modern society? Not necessarily.
Being anxious might have helped my ancestors prepare for unexpected famines. Being aggressive might have helped them lock down the resources they needed to survive.
Do those emotions help me as an adult software engineer in Houston? Heck no. Anxiety and aggression just get in the way of a well-lived life.