I edited this sentence to make it clear that I mean only it in the programming context.
I believe that we could use positive or neutral emotions instead of negative ones, at least in most cases. Curiousness instead of inadequacy as the drive for learning; humbleness instead of shame; desire to make something great on time instead of anxiety.
Of course, the more difficult question is how to do that.
Your personality largely determines your emotions and you can't generate them at will.
"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.
I think this is a good point why it would be good if we, as an industry, accommodate these emotions rather than force them away or pretend they don't occur.
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.
I think you cannot control how you are made, but you can control what you do with it. It's up to you to figure out how to put yourself in situations where your personality will be an asset rather than an obstacle.
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.