I'm not sure I see how changing the period of the costumes could make
Shakespeare's plays more accessible. Modern audiences stare happily
at characters not even supposed to be human, but who still exhibit
identifiable longings and experience moral conflicts. So why is a
trenchcoat supposed to be more accessible than a pair of tights? Or
more or less sophisticated?
I would have been bothered by the anomoly of speech and dress also,
although I did enjoy a simulcast of Don Giovanni in modern dress
several years back. It was staged in an inner-city slum, and the
addition of that context filled out the opera for me in a new way.
Don Giovanni was suddenly someone fighting for the life he knew, not
just for his satyriasis.
So I'm tempted to say: if the costuming and staging ADD to the
richness of the experience, or highlight some important aspect of the
play or opera, then they're good. I suspect that simplicity and
accessiblity as guiding principles will not accomplish this.