It’s “reliable” insofar as it tells us how the “average” person is doing, and by definition the lower bound for the top half of the population.

Not reliable at all if you have a bimodal or multimodal distribution.

That’s not true. As long as you’re taking into account the median purchasing power, it doesn’t matter what the shape of the distribution is.

Real median income has increased regardless of the choice of inflation index.

How so its a much much better measure than the arithmetic mean ?