1. Shakespeare is to modern acting technique as ballet is to other forms of dance.
Whether you are a jazz, tap, contemporary, or even hip-hop dancer, it is best to have a foundational training in ballet. Now, is it imperative to take ballet in order to learn other types of dance? Not necessarily, but it puts you above the rest. Classical ballet training can only help you.
Same with Shakespearean acting. It is one of the most classical forms of theatre. Combining the cerebral aspects of breaking down the complex poetry with honest emotion and humanity can be a difficult process. The concepts and ideas you learn from doing Shakespeare can be carried into both contemporary theatre and TV/Film acting, and being grounded with Shakespearean training puts you several steps above the actor beside you.
2. It forces you to clearly tell a story to an audience, despite the complex language.
If you don't understand what you're saying, then an audience definitely doesn't understand what you're saying. In order to make sure an audience follows a story, each actor has to completely understand their text and make clear character choices based on the text.
If you can help an audience better understand Shakespeare, modern text will be a breeze.
3. It teaches you how to find clues within the text to help build your character, while also making it your own.
Dissecting Shakespearean text is basically like being a detective. Since Shakespeare didn't write much stage direction (apart from entrances and exits) or in depth character breakdowns, he left little clues within the text using punctuation, spelling, and various poetry devices to help the actors understand their role.
Dissecting text in depth like this can be extremely useful in other scripts. Writers today may not seem too Shakespearean, but good writers write scripts in such a way that show us characters' behaviors in little clues rather then just using exposition or in other words, just outright explaining it. You can get more out of a script than you may think, you just have to be a good detective.
4. Line learning!
There is no ad-libbing in Shakespeare. In modern stage plays or screenplays, if you don't get a line perfectly word for word, it's no big deal. Sometimes you are even encouraged to improvise a bit.
Not in Shakespeare. You can't exactly just make up beautiful iambic pentameter* on the spot (unless of course, you can, which is amazing and you should DEFINITELY have that on your résumé) and not to mention, it would be a disservice to change what Shakespeare so beautifully wrote almost 400 years ago. Also, a lot of Shakespearen die-hards might throw tomatoes at you if you don't get it right (just kidding... Sorta).
As you can imagine, Shakespeare line learning is pretty difficult. It's easy to get the gist of what they're saying, but being getting each line word-for-word can take some serious focus and devotion.
Learning modern text will become much easier if you can become skilled at learning Shakespeare's lines.
5. Gender roles are broken all the time!
In Shakespeare's day, women weren't allowed on stage (rude, I know). So they were forced to use men as the female characters. They would dress them up in wigs and dresses and they would speak in high voices.
Traditionally, Shakespeare plays are no stranger to switching it up when it comes to gender. But these days, we have taken it a step further. Many productions have switched the genders of characters completely or interpreted the text to have romances between characters that weren't necessarily intended.
So whether you are playing a different gender than yourself, or changing the written gender of a character, it creates a challenge for you as an actor. Not only are you stepping into someone else's circumstances and personality, but you also have to consider how gender influences your performance as well as staying true to yourself and instincts as an actor (whatever gender you are) with the aspect of a different gender.
Obviously, I'm a giant fan of Shakespeare. It has truly shaped the way I think and work as an actor, and I always find myself coming back to it as a home-base in my acting career. It seems scary because of the complexity, but I promise it's not! The complexity of the language is what makes it beautiful, and after some practice, it becomes easier to understand. Dive in head first and see what you can learn. I guarantee you'll be glad you did.