Hi - as mentioned above the usual reason to want to edit the original invoice (or bill) is to correct simple mistakes, the most common, for me, being the date. I too have made VAT errors by not spotting that the invoice or bill had the incorrect VAT rate but, because I entered the gross amount, the total sum paid off was right.
I'd add that one area in which I would almost always want to edit a bill date is where someone has generated it via the bank screen, ie a PAY document generated by the system when entering a bank payment. In many cases there is a bill in existence, or one arrives late and these can be scanned & attached to the PAY doc but what you can not do (unless you know it at the time of the payment) is to enter/edit the actual bill date, which would, I suggest be non-compliant with VAT legislation.
The alternative to voiding and starting again with an invoice (telling the customer to trash it) is to issue a credit note and then issue a fresh invoice but that's daft if all you want to do is correct a simple mistake.
With regard to the legalities it was far easier to correct a paper invoices when a mistake was made, and I can remember tippexing out numbers and hand writing over them! So, as John says, as long as the VAT return has not been submitted I'd like the ability to edit anything on a document, but with perhaps the only exception being the system generated invoice number?
Finally, what seems a bit silly is that one of the fields you can edit after payment is "VAT treatment" ie I can create an invoice with 20% VAT then, even if paid, I can edit the VAT treatment and show it outside the scope and not to appear on the VAT return. The invoice is updated with the 20% VAT still fixed on it. I dread to think what then happens when the VAT return is prepared.