Yes do away with the chuck and just bolt directly to the rotary platen for greater rigidity and more room.
To be picky your illustration does not show a trunnion table, or at least what my understanding of a trunnion is; I thought the trunnion was another rotary axis in the center of what your picture shows.
We have several machines equipped with what you depict and use them for three sided machining of multiple parts. Actually one setup allows four sided machining through holes in the fixture.
An open mind is a virtue...so long as all the common sense has not leaked out.