In many expensive cities the median compensation is well below the poverty line

Uh, what? Can you name some and provide numbers?

In Los Angeles the median individual income is $30k.

For an individual, HUD puts the "low income" threshold at $70k and "very low income" at 44k.

That's not a good way to think about income because people live in households, and the median income of all individuals includes people who aren't expected to contribute to the household income like children.

Ok.

The mean household income is $70k and the average household size is like 2.7.

For a household of 2 people, the HUD low income threshold is $80k. For a household of 3 or 4 it's $90-100k. Although they'd be a bit above the HUD very low income threshold