Copley was originally designed to have a Boylston Street style underpass for the Huntington Avenue tunnel and a pedestrian stairway between platforms. The offset platforms were going to work something similar to Boylston Street. Unfortunately the Depression and the sensitive foundation of New Old South Church put a serious dent into those plans.
Building a new station under Copley Square is also unfeasible. Not because of the proximity to Trinity Church, but due to the massive utilities which still run under the old alignment of Huntington Avenue under the square. The depth of utilities are why an Arlington style mezzanine wasn't possible.