It depends on the distribution. The reason it is often used is when there are extremes in the distribution like a handful of people paying $1B per year on a property pulls the mean upwards.
Also depends whether you can about the middle more than the 10-20% of the people most struggling who can earn much less than the mean or median
The median alone doesn't paint the whole picture. We need to compare the spread as well. The median doesn't care if you make just under the median, or $1 a month.
When it comes to income and wealth, I don't think so. There aren't enough people in the middle ground between rich and poor for that to be a meaningful stat for most things.
If there are very few people in the middle ground, and more people are poor, then wouldn't the median be a poor person and therefore somewhat representative? I'm not sure I'm following your logic here...
Also depends whether you can about the middle more than the 10-20% of the people most struggling who can earn much less than the mean or median