I think it all depended on the house. I have seen lots of old houses where the countertops were shallow. And have heard that they aren't deep enough to put in dishwashers.
Kitchens back then weren't the standardized 24" deep counters, 12" deep upper cabinets that we see now.
What is strange to me is in older houses, the stove will be on one wall by itself and the cabinets on the wall next to it, run past it, so you'd have trouble getting items out of them it would seem, and to use the counter top there, you'd have to stand with your back to the stove.
Also for some reason, it seems weird to me when the stove is next to a doorway with no cabinet between it and the traffic path, seems it would be easy to get burned with it being there if you weren't careful.