From the show's earlier episodes, it's easily evident that Kaori was a great violinist. Even one of the judges was shocked and wondered like "where had she been all this time and why isn't she famous?"
Why wasn't Kaori famous or known as a notable violinist? Even a popular violinist like Toshiya Miike knew about Kaori, as it's shown in the anime that he dislikes Kaori's playing style and disrespects her in front on Arima.
We do not know Kaori's progress in her violin studies, and as I am not a violinist, I cannot comment on the difficulty of her repertoire (and thus, of the competitions in which she plays). However, there are two out-of-universe reasons for Kaori's lack of fame that come to mind.
Firstly, even classical music listeners might not follow competitions closely enough to recognise those who performed well in them. I mostly listen to classical music and I know the names of a number of big competitions, but I barely know the names of those who did well. Moreover, with the exception of certain "niche" interests — period instruments, transcriptions, some types of vocal performance — I am likely to end up listening to recordings and performances by better known, more "established" musicians whom I already know.
Note also that there are any number of decent musicians who play difficult repertoire but are not well-known outside of their local circles.
Secondly, it is made clear by episode 2 that Kaori does a poor job at following the score, which might prevent her from getting a following in the right circles.1 I might avoid someone whom I knew to consistently and flagrantly push an interpretation that clearly was not the composer's intention, and I am not the only one. My teachers would also be unhappy with me if I played like that, which in turn would inhibit my development and recognition.
She says in the letter in the final episode that it was only when she learned of her illness that she started doing things so she would have no regrets. One of these things that are mentioned is that she started playing the violin how SHE wanted to so that people would remember her.
Because there are countless good musicians who are not famous.
