Shakespeare's plays post-date the bulk of the Great Vowel Shift. The reason they don’t rhyme is only partly because of the very last phases of the Great Vowel Shift, and partly due to the changing English dialectal landscape.
The classic English author for whom the Great Vowel Shift is most relevant, in terms of audiences today not pronouncing the text anywhere near as society then would have, is Chaucer.
The classic English author for whom the Great Vowel Shift is most relevant, in terms of audiences today not pronouncing the text anywhere near as society then would have, is Chaucer.