You are confusing American media with American culture. In American movies of the past the smart "nerds" were bullied. In reality, at least in my experience as someone who was bullied a decent bit, this is actually conflating two separate, but overlapping, groups. This isn't surprising since most foreigners understanding of our culture comes from our media.

In my experience (left high school in the early 2000s), the kids who were bullied were the kids regarded as "weird", smart kids were mostly left alone or blended into popular groups. The "weird" kids were mostly kids with obvious issue. Social maladjustment, visible poverty, autism spectrum disorders, or just being unkempt. There is some overlap here with smart kids, largely due to autism.

The reason this narrative exists is that a lot of the children with issues told themselves they were bullied because they were smarter than everyone else, even though that wasn't the reality. I don't know if this was them internalizing the hollywood stereotype, or hollywood playing to an existing narrative. It's perhaps more tragic that kids who were already at a disadvantage were the ones who were bullied, but it makes more sense and is the actual reality as I experienced it.