All artistic study is rooted in the classics whether we are talking music or art or dance or acting. The major reason that they are studied is that there is not an artistic challenge not found in the classics.
The study of Shakespeare in the training of an actor is necessary and very important. There is not a type of human being and their subsequent behavior or a literary theme that he as a playwright did not address.
In the beginning, the language Shakespeare uses can be daunting but once an actor learns to breakdown the language and understand how Shakespeare is using not just the words themselves but the sounds of words to inform, they become better actors.
One of the hardest things for an actor to do is to release to the language but the rewards are amazing. When an actor stops imposing on Shakespeare and lets the language dictate, Shakespeare is directing.
Once an actor learns classical acting, and I don't mean a classical style of acting, they are easily able to break down the language of any playwright.
Actor only trained in modern acting cannot do classical since they do not understand the language and the demands made by the language. There are numerous examples of this on film.
Studying the classics makes anybody a better musician, dancer, writer, painter, actor, etc.