I don't know enough about Visa's design to comment authoritatively - but my working assumption is payments from issuing to acquiring banks in-country are done net and through visa - i.e. one net payment per issuer into visa and one net payment out to acquirer. e.g. see the last page of this doc: https://usa.visa.com/download/merchants/visa-core-principles...
What isn't obvious to me is what happens in international scenarios - you ask a great question.
Do you see an advantage for bitcoin then by removing the need of peering banks?