The important thing here is the ability to maintain the suspension of disbelief.
When dealing with homogeneous populations, it is irrational to stick someone into the mix that is clearly different from the group in fundamental ways.
An all black "Hamlet" is a reasonable interpretation of the idea, but a patchwork of "diversity" is just silly, especially when dealing with aristocratic families, such as in Hamlet or Romeo and Juliet.
You might have a point if it were a film that went to great lengths to create the historical city of Verona. But it’s a play. You aren’t going there to see a recreation of Renaissance Italy. You’re going there to see Shakespeare. Resetting Shakespeare in different times and places and recasting it with actors of different backgrounds has been standard for years. Take it up with Claire Danes and Leonardo DiCaprio.