We've been primarily focused to date on companies where issuing cards is core to providing their business to customers, for example a startup that provides expensing customers, or a platform that needs to purchase goods in the real world. We're less focused on a business just using it for their own expensing (as we don't have receipt upload functionality, etc).
To your two other questions though:
(1) Could users approve things in real time? Sort of. We provide the ability (as you noticed) through API, but it needs to be responded to in < 2s, which means it's not possible for a human to be in the flow.
(2) Could this be linked to an external bank account? Again, sort of. To get in the weeds: as soon as we approve an authorization, we're on the hook for those funds. A debit to an external balance (or bank account) may fail and Stripe would be on the line. This is why we typically require funds to be in a Stripe account prior to purchases taking place.