The great A Major Piano Concerto, K. 488, number 23, Zoltán Kocsis at the piano
with the Virtuosi di Praga under Jirí Behlohlávek,
recorded live At The Rittersaal Of Palais Waldstein, Prague, 29 August 1990.
Figured bass and the "col basso"
In Mozart's day it was expected that the soloist in these concertos would play in the tuttis, realising a figure bass. In most of Mozart's autograph scores of these piano concertos, the orchestral bass line was carefully figured, and in tutti passages, the piano staves are almost always marked 'col basso'-- instructing the the copyist that the bass line for tutti sections must be copied into the solo part.
Leopold supervised many scores where he put in the figuring himself after the copies were made--so there is no doubt that he and his son expected the soloist to perform a 'continuo' role outside of the solo selections.
There is one example in Mozart's hand, thought to be prepared for an inexperienced pupil, of this continuo part for piano--the C major concerto, K. 246. You can find it in Paul Badura-Skoda's Eulenburg edition of K.246 of 1968 (no.1269)...it's mostly 3 or 4 part harmony, in chordal fashion. Sometimes just octaves, sometimes just left hand doubling the bass line at cello pitch ('tasto solo')
It was later in the Romantic era, especially after Beethoven's death, that the soloist performing in all piano concerti was conspicuously silent, to highten the dramatic effect of the lone voice versus the group.