There was a time when writers separated every clause and phrase with a comma, but it’s now common practice to reduce commas to a minimum and to eliminate semicolons and colons. The effect is to make prose more informal and fast-moving. Lynn Truss, in her funny and clever book, Eats Shoots and Leaves, is generally in favour of the low comma-count.
As the purpose of writing is to communicate – or it should be, because some people write to impress and bewilder – the only purpose of punctuation is to improve communication. It also aids rhythm, but as the purpose of rhythm is to aid understanding, that amounts to the same thing.
Rules of grammar can help tyros who don’t know how to write. In every field of activity, the absolute beginner doesn’t know the rules, the inexperienced person keeps all the rules and the experienced person breaks the rules.
Apart from the distraction value of Therese Coffey’s laying down the law about the Oxford comma, her instructions suggest a lack of writing experience. Her exhortations to civil servants about clear writing are anachronistic, since Ernest Gowers’ guidance revolutionised official communications sixty years ago. Good writers don’t bother about rules like this.