I'm going to go against everyone else and recommend that the pianist "run" the rehearsal. Especially in a piano trio, quar-, quin-, or sextet, the pianist will have the most rhythmically and musically important part.
Take the Poulenc sextet. Every one of the wind instruments is disposable. But if you take out the piano, it suddenly sounds empty.
The pianist, in addition, has no control over the intonation of his/her instrument, whereas the other instruments will. It is thus the pianist's responsibility to have a meticulous ear and guide the other instrumentalists in their intonation.
All of this is feedback I got from a recent master class.