This is a question that is largely based on people's opinion. However, I would say that the majority of people, if not all, would say that William Shakespeare is an excellent writer and that his works deserve to be read and studied apart from the stage. Of course, to see the works of Shakespeare acted out is a treat, but his writings alone are excellent. There are several ways that we can come to this conclusion.
First, truth be told, many schools and universities read Shakespeare without ever enacting his plays. This alone should be proof that his writings alone are excellent and worthy as an object of study and admiration.
Second, Shakespeare also wrote many works that were not supposed to be put on stage, like his sonnets. When it comes to these, what we have to rest on is his writings alone.
Finally, he has passed the test of time. He has been beloved of all generations. This fact alone might be the greatest testament to his his genius as a writer.