I'd never want to send large BTC amounts through visa, but I would trust them enough to facilitate <$100 transactions for a ~3% fee (with some potion profit and some towards tx fees).
Or heck, maybe consumers don't need an actual channel, just let me send Bitcoin out on credit and pay my monthly balance with BTC. Maybe only channels to vendors that receive payments are necessary.
Not sure how much demand exists for this, but "We are the #1 facilitator of Bitcoin transactions" would probably be great for Visa's stock price if they could achieve it.