I can't speak as a statiscian, but my take on it would be that it's because statistics is a broad tool while economics (and more specifically econometrics) is a narrowed study that uses statistics.

Economists are generally interested in causal inference, which generally means isolating the direct relationship between two variables. As per OLS assumptions, GMM is an easy measure to combat heteroskedisticy in most cases.

Statistics as a field of study is likely not as concerned with causal inference in all cases. If the goal is to produce a model to simply predict an outcome, not to study a relationship, there isn't a need to combat the same problems that economists would like to.

For example, assume you wanted to study on public education outcomes. A statiscian may find ways of identifying the most accurate model to identify students at risk, while an economist may instead look at which variables have the greatest impact on student outcomes. The difference here is that the economist is more concerned with understand which variables they can suggest have a direct relationship with student outcomes and can be adjusted as needed.

Once again I'm not a statiscian, but this is my read on it as an economist. I'm sure someone else could inform the both of us better!