"difficulty of transposing on piano"

As a pianist - If you practice all your 36 scales (12 Major & 24 Minor!) every day to the extent that you don't have to think, then you have a basis. Of course, it helps to do all the arpeggios too, and the Hanon helps a lot to... :-)

You see, the black and white notes mean that the fingering for each scale is different. As every piano accordion player knows, jumping to a new set of bass buttons is easy, cause the same fingering patterns for the I IV V etc still work, but you have to put different fingers on different keys when playing the same tune - unlike a "Chromatic keyboard' accordion...

So the next step is practising the transpositions...

I knew an old 'music hall style' pianist - gone now, sadly - who could transpose anything by any number of semitones on the fly... she was about 90...