Different kind of bank relationship. There are two banking roles involved in card networks: merchant acquirers and consumer card issuers. Visa/MC are the intermediary between them.
Stripe only partners with a merchant acquirer bank. To replace Visa/MC they'd also have to get into the card issuing side of things: get a bank or banks to issue "Stripe cards" and get merchants to start accepting them.
Stripe only partners with a merchant acquirer bank. To replace Visa/MC they'd also have to get into the card issuing side of things: get a bank or banks to issue "Stripe cards" and get merchants to start accepting them.