I'd suggest to look at this more generally.
Up to recently, there was science that required one to have a philosophical mind. There were such people, scientists, who thought and felt differently than others, and who were literally a different kind of people, because they wanted to know the hidden truth of things and think more rationally than others who looked only at the surface. They were special people to talk to; they were interesting not only by their deeds like most other people, for example engineers — from whom it is always a result that is eventually required, and nothing else than a result, — but also, and especially, by their words. They could be spiritually enlightening people to converse with, and that was the main value that they brought to the society as a whole: rationality, and education. They could not only give you what you need, like other intelligent people who do not shy away from some work, but they could also tell you what you should in fact need, and what you should think about things in general. To sum up, they knew something, and they wanted to know, and they changed and moulded their minds in order to know, and they strove to know by all ways, all their life. And what they would tell you could well be much better than what you could think by yourself. It was not merely sporadic, there was indeed such role in the society.
Now, such science is gone, or almost gone, and certainly it is being pushed away as philosophical nonsense, or as a violation of liberty, or under many more pretexts. People who take the place nowadays are usually just ordinary people with an ordinary organisation of mind, to the ordinary exception that their mind be well suited to their profession at hand. And that profession has nothing to do with knowing the hidden truth, rather it is centred around deliviring a result, like all other people do. Of course, still someone entering academia might do so because he has a philosophical inkling in his mind, but what matters is that he can do all his duties no matter whether he is a philosopher or not, without paying any attention to the philosophical spirit even if he is endowed with it, and that, therefore, even in the case he is, still his philosophical spirit undergoes no meaningful development during his education and work, his conclusions remain as meagre from the philosophical point of view as anyone else's would be. Quite generally one might say that such people perform the role of, so to say, a meta-engineer: the object of their job is to endow other people of action with ways to go and templates to use.
So there is a mix of the present and of the past. The memories of the past role of scientist still remain. A young scientist can see that he is bright and hard-working, but he also is still taught, often implicitly, that there is something more that is required from him, and he feels, quite vaguely, that he does not possess in his soul that which he should have. He is not that special in his thoughts and in his feelings, he is just like all other people around him, especially like those of them who have acquired, too, a difficult profession: for example, a doctor, a lawyer, an engineer, an economist. What is worse, his own profession differs from most other professions in that he does not deliver any results immediately, his results might or might not make a difference only in the future, sometimes in the distant future. He is like, say, an IT security specialist, who is only thanked in a handful of unlikely events, or even not at all. That exarcerberates his feeling that he is not doing enough.
Now, of course, if he can see his real position, and is not trying to think he is one who he is not, namely a scientist of the past, a man of wisdom, then certainly he shall not feel he is an impostor, and will simply take for granted the contingencies of his own profession. In society, all memories wane eventually, and one of this special role of a scientist is probably destined to go the same path, unfortunately. One might make a prediction that in twenty to fifty years there will be no more impostor syndrome in academia. This is merely a thing of our days, a result of a social change not yet complete.
What does that mean, eventually? That it is actually quite fine not to have any "syndrome", as usual. It should be just like elsewhere: some work, some do not, but those who do not usually leave… or are supposed to.