The bank feeds are provided by Yodlee, who are a third party service. We're not aware of them adding a feed for Stripe as they mainly support the banks and building societies here in the UK and further afield.
We have no plans for a direct feed either unfortunately. If Stripe were to add an automated way of pulling in transactions similar to PayPal, then we could certainly revisit this.
But as I mentioned above, Zapier can almost offer you a live feed if you set it up correctly, as this can just pick up transactions as they happen and create a new bank record.