Your idea assumes that customers are far more invested in collecting / curating / admiring invoices than they really are.

What if a customer is a business or government unit - where A/P is probably handled by multiple people, who change over time? Those guys work by rules & procedures, which are set by some higher-up. Higher-ups usually don't like "we gotta do things different with this one" vendors. Nor to see an A/P clerk futzing with her smart phone yet again, on company time.

Or, what when a customer's CPA wants to see the invoices, to make sure stuff was categorized correctly for tax purposes? "All the invoices from Supplier #123 are in this app, which you'll have to install in your smart phone...". That may not go over well. Especially if the CPA mentions it as a reason for needing more billable hours to do the job this year.