I think it depends how you interpret "and the total VAT charged at each rate is shown."
I assume that it means "is shown in your digital record". This is implied in the explanation in the article.
I would agree and recommend that the invoices be attached to the statement and kept, particularly if more than one VAT rate. This is how petty cash and expenses are commonly dealt with.
Just to clarify, did you mean "....as a blanket for all clients..."?
I agree about the sensibleness.
They really are!
Did you mean "rarely"? I assume you are refering to contractual position and economic reality.