The teaching of Shakespeare should be compulsory.

Shakespeare had a fare more wide-ranging influence on the development of English literature - perhaps in a debate about education in Scotland the point would stand, but in this context Shakespeare is by far the superior figure. 
 
Also, the debate is not about who had more to say that is meaningful to "the common people" but who is more important to recognise as an author. Shakespeare's work is important not only in its content but its wider context as a body of work that influenced later writers.

I would suggest Robert Burns, instead. He had much more to say that was meaningful to the common people.