There is no requirement for a cross to be on the chasuble. It is frequently used, though, in some fashion or another. However, the sets I use for daily Mass are actually completely plain and have no embroidery at all.
In part it is the intersection of the preference of vestment makers meeting the preference of those purchasing vestments. (And the rest of us make do with what we then find those responsible for purchasing vestments have placed in the sacristy’s vestment closets.)
