How I'd redesign a piano, is with the black keys equal in color and shape to the white keys. That way, transposing a song by a semitone is equivalent to shifting your hands by one key. Much more natural. I think they call an instrument with this property "chromatic", but I'm not sure. Actually, perhaps somebody can explain why the black keys were invented. Because their existence makes little sense to me. For example…
- Black keys are a reference. Either by touching them or by looking at them, you can always know where you are. Not so easy with all the keys being the same. - The size of the keyboard is more or less adapted to our hand size. The distance between whole tones is similar to the distance between our fingers. A fifth is as wide as my hand, and I can play an octave without much effort. Making all the notes the same shape would change that and those common intervals would be more difficult to play. - Our hand is not flat. The fact that some notes are higher than others makes playing more comfortable. - Range. Same-shaped notes would occupy more space (unless you make them smaller than white notes, which would be uncomfortable) so either you get way bigger pianos (as if they were small) or pianos with less range.
There are probably more reasons why the black keys are there, these are just top off my head.