The classic example would be the stress response. It's perfectly useful to go into a flight-or-fight mode if you need your body to be ready to escape an imminent threat like a lion you spot in the long grass 100m away. But when you have the same physiological reaction for weeks at a time due to a looming work deadline, this is not something our minds and bodies evolved to tolerate.
"Twin studies and other research have shown that about half of the variation between individuals results from their genetic inheritance and half from their environment. Researchers have found conscientiousness, extraversion, openness to experience, and neuroticism to be relatively stable from middle age through old age" [1]
What if you don't feel any curiousness? Or you feel it for something that is counterproductive at the moment?
What if your desire of making something great clashes with your boss order to make some more boring CRUD software because that's what the client wants?
In these cases, anxiety and inadequacy could be the very emotions that recenter you on what you should to do.
[1] https://en.wikipedia.org/wiki/Big_Five_personality_traits
At the same time, it doesn't have to mean that one cannot improve things independently. We can't change personality, but we can change beliefs, which also affects what we feel.
Consider this: I used to feel really bad about having my pull requests getting reviewed, because other programmers would leave insensitive comments full of criticism. At one point, I just realized that they are not motivated by shaming me, but that they just care about the codebase's quality (and are not very good at conveying emotions in written comments). This change in perception literally changed how I feel about it.
As far as emotions like inadequacy and anxiety, I think mindfulness is a useful tool in terms of differentiating between having those emotions and dwelling in them.
For instance, recognizing one's sense of inadequacy, and from a sober state of mind being able to decide whether that is a signal to reenforce one's skills in some area, or to remind oneself why that reaction is inappropriate in this case is a healthy response. Just walking around feeling bad all day due to imposter syndrome is not a healthy response.
That said, I've had colleagues who could probably do with a bit more shame. Confidence and self-assuredness is great for self-promotion, but if you can continuously produce shitty output with a smile on your face I don't want to work with you.
Depresses people cannot reason themselves to any result at all. Addicted people cannot reason themselves out of addiction. You can fix many things with therapy, but that's far from just "reasoning" and takes a lot of time and work.
Emotions come from a much older part of your brain than the one for your reasoning skills, and thus have a far stronger pull on your actions. That's not to say we are completely at the mercy of our emotions. But controlling them is a matter of practice and reinforcement, not pure logic.
Uhm, not really. All emotions have evolved because they are useful. The ones listed here could keep you from doing something stupid, dangerous, or potentially deadly. They are also likely to make you notice something wrong earlier than others.
Are those emotions not helpful in some cases? Absolutely. Sometimes they are not justified. But that's true of any emotion. Even positive emotions can make you reckless and take too much unwarranted risk.
One might argue that for a programmer those statements are more accurate, but I'm not so sure. Blow some deadlines because of too little anxiety and too many positive emotions and you'll take a hit for sure.