It could also be argued that "medianism" is the perfect method to hide income inequality, because median is resilient to outliers, so the billionaires will not affect the median at all.
Every metric can be "gamed" and so can the median.
Median and mean both compress n data points into one, which is only useful given some assumptions about the distribution. Quintiles (or similar) would work for that scenario, but I'm sure there are more complicated situations where they fall short.
With GDP per capita, a few oil billionaires and a very small class of well-paid oil workers make Equatorial Guinea look like a middle income country. Median GDP reveals that the average person there lives on less than $2 a day, because Equatorial Guinea is also the most unequal country in the world. But clearly it's more representative to class Equatorial Guinea as very poor (median income) than moderately wealthy (per capita GDP/mean income) or rich (per capita GDP PPP)
Median income isn't perfect because it can hide things like one country having 5% living in extreme poverty and one country having 25% but with typical real world income distributions, an average not massively skewed upwards by how rich the top 10% or 1% is gives you a much more accurate perspective on which country most people have higher incomes in.