Until recently, it was a lot easier to lay your hands on a decent set of measuring cups than a good electronic balance. The spring ones weren't very precise, and weights are easy to lose and make a mess. Measuring cups are cheap and simple, and doubling and halving recipes (the most common operations) is elementary-school math.

Even European recipes still measure small amounts for flavors, leaveners, etc. in volumes. A scale that's precise to sub-gram levels is more expensive. So it's not as if you're not familiar with the concept.

Now that electronic ones are cheap it's clearly the better choice, especially for flour, but that's only in the last decade or two. People are switching over to scales, but the volume measurements are perfectly adequate and they're what our existing cookbooks call for.