I think seeing Bridge B from the viewscreen of Bridge A makes it more confusing, not less confusing. I would speculate that reusing the "Mirror, Mirror" extended back of the command chair was a quick, shorthand way for set decorator John Dwyer to differentiate one Bridge from the other so the audience would better follow what was going on. We had to do silmilar stuff to the Bridge when we showed shots of the Bridge of the USS Copernicus
on the viewscreen of the Bridge of the Enterprise
in "Blood and Fire." Doing something--anything--to make the Bridges look different is just one more thing that will help the audicence follow what's going on.