For sake of argument and situational example, these invoices must also be tied to POs which both the buyer and supplier know in this instance will be kicked out of the system for manual remediation given that they also go above a certain threshold for the type of service/widget to be delivered. And let's also assume for further sake of argument that the service/widget is something the organization really does need, and they need it as quickly as possible. I won't tell you that the PO quantity is always exactly the number of dollars of the project -- or simply "1" if it goes about a certain threshold. This goes without saying in too many organizations that we all know of (even for services, which requires an entirely different SOW orientation to effectively manage).
What happens next? Based on personal experience, the buyer and supplier work out a system together to create a series of POs with requisite E-invoicing submission under a certain threshold (e.g., a $100K consulting pilot becomes 11 smaller POs with required E-Invoicing). Or, perhaps, a consulting assignment becomes a contingent staffing project because of certain approvals and requirements. Regardless, the result is that both the buying and supplying organizations lose visibility into the type of detail that properly implemented E-invoicing, P2P, services procurement (with invoicing tie-ins) and matching systems enable all to enable a workaround to company policy.
In other words, the very nature of E-invoicing and related programs can be counterproductive when it comes to the visibility and efficiency they seek to create, depending on corporate policy. So as a supplier, just because your customer is going down an E-Invoicing and perhaps broader P2P procurement path, don't assume that the implementation of such a program will drive efficiency for your operation. In fact, such programs may very well require the creation of additional steps to get around the ridiculous bureaucracies that new levels of control can enable in certain organizations.