This is a very population-density-driven thing. Like Starbucks and being standalone buildings with drivethrus vs just being in strip malls. In cities like LA with significant sections of density but also a ton of surrounding burbs you'll see both; in newer burb-only areas, you almost always have the drive-thru.
My local bank has a pneumatic tube. They have a limit of how much cash they'll send through at one time, a few thousand dollars. If you want more than that they're willing to send it in batches. The only reason I've been able to think of is something involving insurance/liability if the tube gets stuck with the cash in it, perhaps to limit the amount the service tech could possibly lose or steal. I should have asked the old manager about it before she retired, she loved to talk shop.
In Texas we have drive through liquor stores selling closed bottles and that doesn’t seem too bad, but there are also drive through cocktails (like margaritas) and that always seemed like a bad idea to me. Everybody knows they are going to be consumed on the road.
Ours are basically just normal booze shops. Most people would be buying slabs of beer, bottles of wine, etc. Definitely convenient when you just need to grab something on the way to a party or a dinner or something.
From my midwestern US perspective, banks downtown tend not to have drive-throughs, and banks that are in lower-density areas always have drive-throughs.
But then, my perception is clouded by my own bias, wherein: I've spent most of my life in areas with zero public transportation and that generally despise pedestrians.
In areas where people tend to walk, bike, or use public transit instead of owning and driving a car, I can imagine that building a drive-through for a bank has very little utility to the bank or the bank's customers.
The lane closest to the bank had a teller, but the other lanes all used pneumantic tubes to send paperwork and money back and forth.
That said, I wonder if pneumatic tubes have been going the way of railroads - extremely useful for their "right-of-ways" to run fiber.