Absolute poverty is the important measure. If I'm hungry, I'm hungry, no matter what my neighbours have. But if I have a 50" flat screen TV, and my neighbours have a 100" flat screen TV, that inequality does not make me poor. I can still watch TV.
Then the solution is to build more housing, so that supply increases the point of making it cheap again. A lot of housing scarcity is caused by zoning regulations.
Wrong. If you do not have have what the average person in your society has, you'll struggle to participate in your society (in an absolute sense) and you'll be treated as an inferior, which does all kinds of harm (in an absolute sense).
If I live aboard a ship, I am not in poverty because I do not own a car, because in my society, you do not need a car. But if I live in a city with no public transport where you need a car to get around, but I can't afford one, I absolutely am.
Poverty apologists always bring up TV as an example, as if poverty is about optional extras rather than basic dignity, respect and participation.
I don't think you really want to go down that road... Historically, most societies have "chosen" a set of expansive "rights" for the top and limited rights for the bottom. I say "chosen" because most societies had it chosen for them by whoever conquered them, or at best, the lower classes had it chosen for them by those with power.
Many people do think about starving kids when they hear "poverty" though. There would be much less outcry in media if everybody realized it's about kids having smaller TVs rather than truly starving.
There's a running joke in my country that US poverty is our middle class - only two cars and a small house.
Meanwhile in most developed countries, inequality is grotesque and the consequent poverty is on the rise.
*Absolute poverty would decrease much faster if we exploited and expropriated from developing countries a little less.