I find that it goes away with experience. Over time we learn that the true value in our output isn't to ourselves, it's to the users.
I see users of a simple file parsing utility that took me an hour to write gushing over the amount of time it saves them every day and it just makes me feel good to be able to help someone with such little effort.
Not everyone is the same, for some it doesn't go away as easily. I've heard plenty of stories from talented artists, makers, and devs of falling into that mentality. It can be difficult to kick for the reasons I laid out. When it's hard it feels like you're a fraud, when it's easy it feels like you're cheating. It's not true, but people should be aware that these sorts of feelings are pretty common.
I'm reminded of the scene in Office Space where people are brought in an asked to describe what they do. That sort of thing is harder than one may think, it can be difficult to fully sum up how one works and in what ways one's skillset and expertise is valuable. For several years I had a job that was very difficult for me to describe to others succinctly. Mostly because it was hard to explain what I did if you didn't know many other details of the development process within the organization, some of them highly technical.
To use an analogy, it's a bit like asking why Beethoven is good music (without falling back on popularity). To express such things succinctly can be quite difficult, more so if you're put on the spot. Most people don't spend hours and hours thinking about how to justify the value of their own work, because that sort of thing can seem egotistical, more so if they already suffer from imposter syndrome. And without doing that when they put themselves on the spot they'll fall into the same trap of not having a good answer.
I see users of a simple file parsing utility that took me an hour to write gushing over the amount of time it saves them every day and it just makes me feel good to be able to help someone with such little effort.