A Failure to Distinguish
If you advertise your film as having won X number of Academy Awards, I may be attracted to the spectacle, and when I see the film at my local cinema, I will see ALL of the work that won the awards - acting, direction. cinematography, script, etc.
If you advertise your non-New-York production of a play as having won or been nominated for X number of Tony Awards, I may be similarly attracted to the spectacle by the whiff of celebrity in the air, if such is my appetite. But when I see your local production of the play, I will see NONE of the work that earned the recognition, except in the case of a nomination or award for Best Play, i.e. for the script itself. The rest of the work - acting, direction, design - will be different. It will be possibly as good as, or even better than, the work in New York, but it will not be the same work. So where's the logic in selling the play to me as though it were an immutable package like a film?
We celebrate the difference between the theatre and the cinema: I can do things in each of them which I cannot accomplish in the other. Two wonderful arts with quite different strengths. Maybe we ought to honor that distinction on the marketing front.