No one can play the part of Hamlet unless they are Danish.
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.