The reason I'd disqualify it is because part of the design brief is that no person is to be part of the design. Surely Shakespeare is, or was, a person. Anything related to just one person will almost certainly be automatically disqualified.
I don't think Shakespeare is a symbol of the English Language. He wrote in English, he was the most successful English/British author, but he didn't exist in a time of the United Kingdom. His Queen was Queen of England and Ireland, not of Scotland.
Like I said, Shakespeare is the best known English writer, Dylan Thomas write in English, Robert Burns on the other hand wrote in Scots language.
But already we are showing why Shakespeare can't represent "Britishness", it's too contentious. We could go on all day about this. If the press had to release a coin on Britishness that was so contentious, the Royal Mint would have egg on their faces.
4 coins of 4 of the most successful writers, one from each country, fine, but just one, it wouldn't work.
Cervantes can be on a Spanish coin, but not Shakespeare on a British coin. It's just the way it is.
If you want a coin about the English language, it's still going to be contentious, because it's not the only language in the country. It's fine to use just English on the coin, but for the coin to be about English, wouldn't go down well either.
Does it unite? Sure, at times, does it separate? I've lived in Wales and seen how it can.