Umm, yes it has. Anyone who can play a classical instrument and understands classical theory can improvise in a classical style, how do you think most composers write music?
I have seen classical improvisation and known people who do it, some as part of their performance.
However, it's not like "improvisation" in rock, jazz blues:
(a) It's structured. The song has a pattern, and the improv must fit that, like not just rhyming but staying in meter (no rap artist does this).
(b) In addition to harmonic correspondence, there needs to be melodic correspondence
This is far more complex than what popular musicians do, and more challenging. It is however harder to perceive the subtlety of, because nothing's going to hit you over the head with HAY THIS IZ IMPROVIZED like a totally random solo.