From my UK viewpoint, drive thru establishments that aren't fast food are definitely... odd, and like it or not, on the surface they do conjure up an image of "what, people can't be bothered to get out of the car?" whereas I'm sure if you dig deeper there are logistical reasons for it.
However, in thinking about it, American towns don't seem to be set up the same way ours are (I'm not even sure what the average town or city centre is like there - I have images of everywhere having strip malls and no town centre to speak of). We have banks on every high street and shopping centre so it's easy to pop in while you're in town. There aren't the same amount of local banks that you guys have - they're pretty much all high street chains. The banking system also seems quite different - we tend to have our wages deposited automatically and pay everything by direct debit, while the US banking system seems to lag behind in that respect with some people still having to deposit a paycheque and write cheques to pay their bills. So, I can see there's more need to 'go to the bank', whereas here, well - I can't remember the last time I even had to set foot in one. Everything's done automatically and I keep an eye on it with my online banking.
I can see the value of a drive through pharmacy - I hadn't thought about the sick kids, but that's a really good point.
The only drive throughs I've ever seen here are McD's, BK and KFC.