"couldn't improvise from chords on the piano even though she had lots of training. Yet when she took up harp, the improv came easily"

Ah - Funny that - always felt 'clamped' with the piano forte, but ok with the pipe organ, and funnily the harpsichord was easier too... :-)

Now the physical sound production is different with the different instruments, eg the piano is a percussion device (which can change volume by touch [force/impact changes] thru the keys), the pipe organ (and now I find the piano accordion almost like a 'chest-pipe-organ'!) is a wind instrument - effectively an on/off (no touch [sensitivity] control via the keyboard!) switch for the keys... the P/A uses bellows control, while the pipe organ uses additive/subtractive mixes of ranks of stops for volume, as well as 'swell boxes' - ranks of pipes in enclosed boxes with shutters to open.close that affect perceived volume.

'Electronic simulations' can only 'fake' so much of the pipe organ and P/A ... and not very much or very well if you have been properly trained on the real instruments (this includes 'midi-accordions' too!), but in spite of that, funnily enough those 'touch sensitive keyboard electronic pianos' ARE surprisingly 'adequate simulations' of a REAL piano forte. :-)