There are such things are Chromatic keyboards (for instance, the Chromatone synth had one), and there was the Janko piano keyboard and there are people that have made keyboards without the spaces in at the B/C and E/F at the back of the keyboard by alternating the white and the black keys such that those spaces just disappear.
The advantages are:
- you need less reach for the same chords
- transposition becomes trivial
The disadvantages are:
- your muscle memory will be invalidated
- the number of instruments set up like that is really small
- no accomplished pianist will want to switch
But if you really wanted to you could adapt an existing instrument to use a different keyboard and it isn't even all that complicated (medium complexity wood working project).
The advantages are:
- you need less reach for the same chords
- transposition becomes trivial
The disadvantages are:
- your muscle memory will be invalidated
- the number of instruments set up like that is really small
- no accomplished pianist will want to switch
But if you really wanted to you could adapt an existing instrument to use a different keyboard and it isn't even all that complicated (medium complexity wood working project).