Do you think the measure of the lowliest full-time annual wage in the entire economy is the best measure of an economy and job market as a proxy of facillitating a good general Qwuabity of Life?
The lowest are likely to have serious issues and not be particularly helpful (how well the paperboy, special needs cashier etc is not particularly representative or useful.)
We also have measures that capture most of what you're looking for there in the poverty rate.
What might be helpful is stuff like the interquartile ranges (think medians but more of them) or specific medians e.g., what's the median for the bottom twenty, bottom forty etc.
Measures at the extremes are rarely very helpful except for arguing in ignorance or bad faith.
It's not a bad measure but I don't think it's the best, I'm currently working my way through Spirit Level and so I think some measure like the Gini coefficient would be important.
I think that median income, Gini coefficient, poverty rate and something like the human development index would give a decent overall picture. I don't think a single metric really does the job.
I mean, you'd also need to take into account cost of living, the rate of un/under employment, hours worked per week, working conditions in general, and a bunch of other stuff.
I think it's a great idea. And all the people in this thread pointing out it wouldn't be perfect are ignoring the glaring imperfections of "household median".