The point of the sales invoice is to create the obligation for payment. Each invoice stands alone. In many cases, you have no idea (a) how the customer will process the invoice internally or (b) whether your customer might have to provide a copy of the invoice to its customer (such as when you are a 2nd-tier subcontractor to a 1st-tier subcontractor). You would not want information about unrelated jobs cluttering an invoice or revealing proprietary information about other jobs. And your customer might need to keep records separately for different jobs.
The statement, on the other hand, is a summary of what is owed, including the sources of the obligations (the various unpaid invoices).
So I think it is preferable to keep things as they are. That gives users the freedom to adopt invoice or statement billing practices as they see fit.