There are lots of ways to more accurately describe, whether with statistics or with prose, the state of the world. But that would go against the interests of the ruling capitalist class in portraying capitalism as, at the very least, the least worst option.
I would say it has to do with the Marxist understanding of cultural hegemony. The ruling class determines, based on their class interests, the cultural norms, such as the way we typically frame facts and figures. It doesn't hurt that media and academia is controlled by the ruling class and used to reproduce the ideology.
Political reasoning aside, it's also much easier to estimate a mean average from smaller samples than a median without strong assumptions. If you're like the IRS with effectively complete data on tax returns, it's easy to use medians though and there's no excuse.
With a normal distribution, the average is good. With a skewed distribution, the median is okay.
But to get a better idea of the skewedness of a distribution, you need the mean, median, and stdev.
I mean, they don’t always use the mean, and they don’t always use an average as a proxy for normalcy. And sometimes the mean is a better choice than the median.
I don’t know what to do with overgeneralized, hyperbolic questions like this.
I think many times it is presumed that things are of a normal distribution thus median and average are interchangeable.
There's plenty of good answers already, but a big one is that the writers don't know any better, and not understanding the difference of average, mean and median is one of the most common mistakes to make