Well...
Actually a big part of the great Jazz Piano Stars were classically trained : Bill Evans, Keith Jarrett, and now Brad Mehldau, to mention a few.
I think the issue is rather related to some kind of snobism. Unfortunately, even today some classical teachers consider Jazz as "inferior" compared to the "sacred" classic repertoire and then don't bother initiating their students to Jazz (because they don't like it and they didn't bother knowing about it).
Beyond the music in itself, there is a huge difference of philosophy between classical performance and Jazz performance. In classical, there is a huge emphasis on the composer, over the interpretor. A lot of people consider that the performer is in the service of the piece (and its composer). Jazz is the contrary, it is not so important that Moon River was composed by Henry Mancini. Moon River will just be a "tool", a pretext for Brad Mehldau and his trio to let express a flow of musical ideas from their very self, according to their mood of the moment. They build a "piece" in itself, a piece which is played one and only one time in eternity.
Also, playing jazz requires the acceptance of dealing with the very deepest part of yourself. In classical, you have much more interaction with external elements : the score, what you know about the composer and his "manière" et al. So as we see there are huge differences of personal approach of the music, which probably seems dissuasive for some exclusively classical musicians.
The technique of improvisation in itself (if there is any) is only the emerged part of the Iceberg.
Ps : Moon River by Brad Mehldau's trio can be found on "Art of the trio Vol.2, Live at the Village Vanguard".