I've researched the issue...
Since it's not an issue at my bank (because we offer walk-ups and bike racks), I had to research the issue a bit more.
Insurance policies do not generally address bicycles specifically.
However, they have general provisions to mitigate avoidable hazards.
While we are focused on the hazard associated with cars in the queue, the actual perceived hazard in drive throughs is OIL...It was interesting that the hazard is perceived by the insurers as being equal to walk-ups, and any two wheeled vehicles - including motorcycles.
Interestingly, we would serve someone who walked/rode up to the drive through...but we have a very regular clean-up program for oil in the lane;) We're also the first in the entire city to have the sidewalks cleared of snow in the winter:D
So, that's the rest of the story. It is insurance driven in a general sense...but more driven by laziness in cleaning up the oil...