Yes, of course everybody has to have the softer dynamic levels in their voice. However, what is piano for some of us is mf or ever forte for some untrained voices. Remeber that Bel canto arias were sung WITH an orchestra and the pianissimi were heard OVER the orchestra. Do you honestly believe that the pianissimi most choir directors demand from singers would be heard over an orchestra?
I can sing piano. Piano for Verdi, Strauss, Wagner, Bellini, Berlioz. However I cannot effectively sing at the pianissimo level demanded by some choir directors. Well, most of them cannot sing my forte so we are even :)