A more interesting debate is the one currently bubbling away on the classical music scene.
Up to about 120 years ago, improvisation was the norm, so your 'classical' musicians at the level of soloists would be expected to be able to extemporise and innovate on the hoof.
It was only during the 20th century that playing by the score became de rigeur; rather like the standardisation of all the variations of Shakespeare's plays (many of which had been cut and pasted with each other or had large chunks by other writers inserted by 1900).
Just as theatres like the Globe try and recapture an 'authentic' Tudor performance, the debate is now should improvisational skills be taught as part of a classical music education and brought back into performance.
The mere existence of this debate suggest that, at present, formal musical training does, at least discourage experimentation - at least among performers, if not composers.