What if the music uses transposing instruments?
What if the music is polytonal?
You're taking your limited view of piano grand staff, treating it like a single stave, instead of two "players", your right and left hand, and then imagining a notation scheme that won't work for a lot of instrument combinations.
Just to be clear that we aren't talking about something that applies only to unusual scores, here is an example from a set of minuets by Mozart, K. 568...
...where three key signatures are used, zero sharps/flats, one flat, and three flats. Three key signatures are used, because the wind instruments transpose. Sometimes a score can have key signatures using both sharps for some instruments and flats for others, depending on the instruments. Here is an example from Brahms, Symphony No. 2...
D major, but notice the three key signatures: two sharps, one flat, and zero sharps/flats.
The basic idea is each staff represents an instrumental part, and those parts must be given their key signatures, which may differ from other instruments.
Think of your piano grand staff as two instruments, your left and right hands, but because those two "instruments" don't transpose, they will have the same key signature.
The fact that your key signature sharp/flat count doesn't differ between staves for piano, doesn't mean that's how it works for other instruments.