Wayne, my guess would be that cost was a major factor in the usage of
cast iron.  Particularly when one considers that (refined) aluminum was
once very expensive; it was not until modern methods of refining were
developed around the end of the 19th century (I think) that aluminum
was cheap enough to be considered for large quantity fabrication.

Also, I would imagine the casting technology was much more developed
for cast iron than aluminum when pianos (as we know them) began to be
built en mass.  Cast iron has become the traditional material for piano
plates and is still cheaper than aluminum.

Could plates be made from aluminum that functioned as well as cast
iron (sonically speaking)?  I seem to recall reading something about
a piano maker that did try and that the results were less than
spectacular.  If so, this might not necessarily be the fault of the
plate material itself but poor design.  As for making pianos/music
boxes lighter, I doubt most people would have paid a significant
surcharge for a lighter instrument.

Michael Concordia