If this isn’t clear, @Shostakovich, despite the tone of some responses, I suspect (I hope!) that no one here is denigrating the idea of polytonal music, which by definition will be pan-diatonic rather than tonal. (In the case of true tonal music, independent key sigs would, of course, be not only meaningless but absurd.) After all, Stravinsky, Ives, Milhaud, Bartók, et al.…
But of those listed above I believe only Bartók “experimented” (famously/infamously) with disparate key sigs (EDIT: like the OP posed) in, for example, the two hands of some of his Mikrokosmos pieces. Stravinsky and Milhaud both chose a common key sig and used accidentals, I believe.
I’m actually of two minds about this myself:
On the one side, the point of music notation is to communicate the musical idea(s) to performers efficiently. So if a pianist’s two hands will consistently be in different scale-areas, then different key sigs could make good sense, pace Janus above. (And if there’s any doubt, a simple performance note would suffice to clarify.)
I personally, when reading through some Mikrokosmos pieces, have no trouble holding onto the idea of separate keys (though the atypical key sigs are another matter…), and appreciate the visual clarity of not having so many accidentals. One proviso: each hand’s material would probably have to stay in its discrete staff on the grand staff.
On the other, the point of music notation is to communicate the musical idea(s) to performers clearly. Here’s where some of the concerns raised above come into play.
I’m curious: what is/are the musical context(s) in which you want to use them: solo piano music? other?