Nice idea. I have seen a novel (to me at least) system when visiting Boston, a city of traffic jams:
People wearing a metal contraption on their backs that makes them look like ghostbusters. In one hand is a hose from which they can fill your cup; on the other side is a tube of paper cups if you don’t have one. They just walk through the traffic jam (I saw this at the end of the tunnel leading to East Boston) and driver would wind down their windows.
On one hand your scheme has much less labor, but this approach can serve many more, and captive, customers at a high density time of day.