My understanding of the business model for these account aggregation tools is mostly marketing related. They will see that you make payments to Barclays, Chase, etc. and that will influence offers you get at some point. They might also see some payments that could be done via AmEx instead to suggest converting. I don't see it really useful for existing account management.
I think AmEx needs to do a better job about specific benefits to the customer for allowing this option. It might become mandatory at some point, but I don't think it is likely.