Pinchas Zukerman can play both the violin and viola; but of course, that's not the same thing as playing both the piano and violin. It's more or less comparable to playing both the cello and double bass ...
There HAVE, in fact, been versatile musicians throughout history, capable of playing diverse instruments; but it's difficult to see that playing on the one necessarily *interferes* with his ability or development in playing on the other. If anything, because the piano and violin are such contrasting instruments, it shouldn't be an issue.
It's probably just a matter of time and economics: try working out the logistics of managing two full-time careers as a traveling world-class concert pianist (e.g. Evgeny KIssin) AND a traveling world-class concert violinist (e.g. Itzhak Perlman).
I sometimes wonder, for instance, how it is that Daniel Barenboim manages both a piano and conducting career; it's probably a matter of splitting duties. If I understand correctly, Vladimir Ashkenhazy has basically abandoned his career as a performing pianist, and devotes his full time to conducting.
Changing careers happens all the time, whether in sports or music. But one thing you almost never see in today's world is great pianists turning into great composers: in the past, it was almost a given -- and in fact, nothing really builds a legacy as writing something great. So conversely, most great composers were great pianists (notable exceptions being Wanger, Verdi, and Berlioz); it's just that their composing careers overshadowed their performing.
Many professional ballplayers who find it difficult to get away from the game, after retiring, turn to coaching, managing, or broadcasting. However, what I've noticed is that they're not always good at it -- even though they may know the game well. Conversely, a number of Hall-of-Fame (or near HOF) managers had surprisingly modest -- if not pathetic -- careers as players. Examples coming to mind are Earl Weaver, Tommy Lasorda, and Sparky Anderson.
But then, perhaps this is more comparable to how great pianists don't always make great teachers. Say what you want about the piano, but there have been noteworthy violin teachers (e.g. Ivan Galaiman and Dorothy Delay) who didn't have especially remarkable playing careers.