This entire topic is a core treatise of Harold Schonberg's book, The Great Pianists.
If anyone's interested here are some of its ideas.
Schonberg says that before around 1900 virtuosos played compositions anyway they felt like including rewriting, adding, subtracting, changing entire sections of compositions or mix movements from different sonatas, from different composers.
In a nutshell, Schonberg puts forth that the romantic virtuoso saw themselves as the center of attraction, and the music was there to highlight themselves. They played as they felt the music should be expressed. By analogy, there is no way to recite Shakespeare, so its up to the actor to breath life into the words, formulating a general idea of how a particularly scene is supposed to be convyed.
In that view, what one experienced in a performance was always 'unique', that the audience could look forward to surprises. There was a lot of showmanship among this set, and it reaches its apogee with the Liszt school of pianism.
Around Clara Schumann's time, she put forth that greater fidelity need to made towards expressing the composers intention as best as possible, and not to change what is obviously written into score. This is where we are today.
My thoughts:
Schumann's concept maybe a core reason for the stagnation in classical music, and a continuing decline in interest in classical pianism, and piano sales. The emphasis is on preservation, or re-enaction, repeating the same item faithfully over and over, like a museum.
However, a note on music fidelity. A composition cannot have new notes written into it and still be called a Chopin waltz. It will be like the romantic pianists of old did when they rewrote the music, now called, for example a Godowsky transcription of a waltz.
https://www.bmgmusic.com/acq/default/index.jhtml;jsessionid=AGABEP45XZUBECTI0UTSFFA?acqlinkback=y&_requestid=66795I think the time has long been overdue to reemphasize a pianist's more personal view of classical piano music interpretation but not to the extremes of the romantic virtuoso, for 3 reasons.
What has developed in modern pianism is only a very narrow range of interpretable variations, so for the most part nearly all performance is pretty much identical to the general audience.
Second, classical piano students focus on faithful execution of notation over performance passion. The net result is most performances are musically boring. By contrast, 'pop' music is passion first, virtuosity far second.
Passion is discussed by Schonberg and is taught by many good pianist-teachers. One gets it through an extensive and involved experience of
real life, a pianist is unlikely to convey more meaningful feelings through performance, if they don't have complex and vivid feelings themselves.
Third, playing strictly by notation creates a standard performance type dictated by the notation. Piano competitions encourage a partciular pianism as decided by judges which, coming from standard music school ideology, continues the status quo of music interpretation. The word conservatoire comes from conserve or preserve, not to breath new life. And aren't most preserved things already dead?
Conservatory \Con*serv"a*to*ry\, n. [Cf. F. conservatoire, LL.
conservatorium.]
A public place of instruction, designed to preserve and
perfect the knowledge of some branch of science or art,
esp. music.
When you look at classical pianists willing to risk idiosyncratic interpreations, such as attempted by Glenn Gould or Lang Lang, you will certainly get harrumps from the professors and audience members expecting a standard interpretation. But I think angering such conservatives is worth it in trying to appeal to and create a bigger general audience. There will always be room for the academic interpretation as desired by Clara Schumann, but that is probably best left within schools and 'authoritative' performances.
If you can find old recordings by pianist who were students while Liszt lived, the true romantic pianists such as Josef Hoffman or Vladimir Horowitz, you'll find they did take much more liberty in interpretation than we do today, and their playing is far more livelier, unique, and engaging, than a lot of what we hear today.