Not "fair" at all, and not at all appropriate. Still want the average, the mean, the expectation because of the law of large numbers and the best L^2 approximation property of the mean. Besides, often in practice, e.g., for even positive integer n independent, identically distributed samples from a distribution absolutely continuous with respect to Lebesgue measure, the median is not even well defined.
The median is good for politically correct news stories about data from political economics.
No, as is clear on the screen in front of you, you wrote
"I think it's fair to assume"
No it's not "fair to assume" that.