Improvisation demands an intimate rapport with the performer that a proscenium blocks. It also is a small scale or solo effort, the more people improvising at once, the greater the tendency towards entropy. And finally, the pleasure in improvisation work can be greater for the performer than the audience, especially if the performer forgets to build that essential rapport. The danger of masturbatory noodling about the stage is great. Improvisation is not antithetical to classical forms, but it is more strictly governed by a controlling framework.
Good examples are piano cadenzas or baroque ornamentation when playing an instrument.
The written score of the second movement of the Brandenburg Concerto is two chords, which some very cowardly groups have in fact recorded without any of the improvisation so obviously intended to be placed there by Bach. The structure is still clearly outlined. In classical ballet, there exists a rare, but prized species of improvisatory dancer of that nature. Suzanne Farrell and Darci Kistler are two of the first who come to mind. It should be a rare bird, the risks involved are quite great.