Storing invoices is not a differentiator: every product does it and most organisations already have somewhere invoices live. What separates invoice management systems is whether they hold the things a person produced once and would otherwise throw away, which is what makes the record worth having a year later.
The match result, kept
Whether the invoice agreed with the order and the receipt, and if not on what. In most teams that answer is worked out once, by a person, and then lives only in their memory until the next question forces it to be worked out again from the documents. Keeping it is keeping the expensive part of the process.
The exception reason, attached
Price variance, quantity difference, no purchase order, no receipt, unrecognised supplier. Recording the reason converts an undifferentiated queue into routed work with owners, and it lets you count reasons monthly and see which upstream problem is generating your workload. That count is what changes other departments' behaviour.
The approval and the versions
Who approved, when, for how much and against which documents, held outside anybody's mailbox. And each reissued invoice as a version with its date rather than as a new document, so which one was paid against is answerable. Both are cheap at the time and near-impossible to reconstruct later.
Questions people ask about invoice management systems
Is this what accounting software provides?
It records the accepted transaction. This covers the stretch before that, where the delays and the exceptions live.
What is the minimum useful system?
A record with supplier, amount, dates, status, owner and the document attached. That alone replaces a shared mailbox and a spreadsheet.
How long should the record be kept?
With the invoice, under your own retention obligations. The approval history is part of the record of the transaction.