Interestingly, one of the major contributors to the original OED was a prisoner who had lots of time to read lots of books and research first uses of words. He

Interestingly, one of the major contributors to the original OED was a prisoner who had lots of time to read lots of books and research first uses of words. He had a prodigious memory as well. I suspect Shakespeare gets the nod so frequently because he wrote a lot of stuff in Early Modern English that survived and was widely available in the 19th century when work on the OED began. Other writers' works were extant, but not widely read or available. The OED notes the earliest printed use of the word meaning, so even if perhaps some dullard like Algernon Sidney used a word first, almost no one actually reads those works, nor read them in the 19th century.