Property market

If you own your own Home, you are very unlikely to be in the "living in Poverty" group.
A current home owner only becomes rich if they sell. Not everyone wants to move to some small town beyond the Black Stump, which is where you have to go to be able to get a cheap home and there may not be the work available.
In the meantime, those that have Homes that are now worth over the mill, now have higher rates (or will do), higher insurance etc. Those wanting to buy fir the first time can't and those than managed to swing it with the Banks, now have mortgages that make your eyes water. Those that cannot buy are stuck in Rentals with Rents even higher than mortgages.
It is no where near as simple as you suggest.

Wait for the upcoming property market crash....for those who have borrowed and bought in the last 3 / 5 yrs.As stated you only 'profit' if you sell and don't replace....or move to a cheaper area.

The govt shouldn’t be in the business of building houses itself to solve this problem but instead creating the most favourable conditions to incentivise private sector to build right kind of houses in right areas.

In other countries this includes things like forcing developers to build a representative mix of sizes & prices to be given consent on a given development site. To avoid them catering to the top bracket only.

Also, governments have encouraged creative new techniques like converting an old airfield into a private development site - allowing private individuals to buy a plot at low price and skip many of the normal rules & hurdles to encourage highly creative, individual hone builds. These are often taken up by young couples who otherwise couldn’t afford to build or buy via traditional routes. It also encourages creative flair resulting in some amazing variety of designs side-by-side. As opposed to the depressingly repetitive housing estates popping up all around Auckland.

It just takes some more imaginative policy to try this stuff.

Therein lies the problem.

By providing State Homes, you help lift people out of Poverty. Our Country was built on that very thing of providing State Homes. My Parents got their start in a State Home. They were none of the things you list above of course. They managed to make something of themselves, but it took a tremendous amount of hardwork and sacrifice.

Families living in Poverty have a higher chance (statistically) of falling into one or more of those catergories you list. By finding as many ways to get them up out of poverty means we (as a Society) can get these poorer folk up out of poverty and hopefully reduce the Crime Statistics.

But there is also a problem now with State homes of the 50's/60's. They were built side by side, resulting in the creation of large communities of low Socioeconomic Families. In some Cities of the World, they are called Slums. Rank with crimes of all types.
As NZ State Homes became old and tired and other more affluent areas popped up with flash wealthy People in flash wealthy Homes, we simply and to a point, unwittingly created the slums of today, where we have division among Rich and Poor, areas of poverty, high unemplolyment and bordem that leads to crime and so on and bingo, we have these problems in Society today. But that is not to say Wealthy Families do not have their problems either. You still get "Rich Kids" doing Drugs. We all know wealthy people getting into serious drugs and crimes.
So in recent years, the Gvt figured that the way to stop most of the old State Home issues, was to allow Developers to build flash suburbs, but ensure that lower price Homes were also included within the Flash Homes. One of the first was Hobsonville, site of the old RNZAF. But I think one major mistake was made. The Gvt decided to sell the sections at a premium. the developers had to build minimum value Homes and there were very few cheap homes built in the end. Some would even argue that the type of Home built, the High density type design, will only produce the Slums of tomorrow.

What I am trying to show and to say above is that the problems are vast and varying. Scooner, your assumptions and your ideas of how to solve are far to narrow. It is complex and the one thing I do agree with you on, is that providing State Homes alone, is not the fix. In the end, the cost of Home ownership is out of reach for the vast majority. Problem is, there are few Alternatives. If you rent, you are trapped. Making Home Loans tougher to get will not help the problem. It only makes the other issues worse. Very simply, Costs of Building are too high in NZ for a nyriad of reasons. Cost of buying Land in NZ is far too expensive due to all the red tape and the cost of development today. Things are not being helped by the difficulty in getting building products at the moment.

And finally, we as a Country do NOT want to see House prices Fall. The damage is done. They must maintain their price, because if Homes were to drop in Value, we end up with a major Financial crises on our hands. The only way to solve the situation is to have Peoples incomes lifted to meet the cost of Homes. But that is not so easy and painless either. Simply, we are not building enough Homes in NZ to meet the demand. Meeting demand means prices will plateau. We have just started seeing that in many areas of NZ, but it is caused by many locked out of the market by the Reserve Bank lending rules to Mortgage providers.

You overlook a lot in there G. i'll try & cover some of that. First the State House era was post WW II & all that brought. Refugees who wanted to work ,save and rebuild their lives. 10 pound poms poured in. Land was carved up with few infrastructure amenities = low cost.Section cost probably around 20 % of home. Mostly larger sections too which subsequently got subdivided off to create huge load on inadequate infrastructure creating compression of population which can cause friction. Those old Beazley,Keith Hay houses were well built too,unlike the leakers of the 90's. Crime doesn't necessarily follow low socio economics either. Witness John Key for instance but lack of education can be a major factor. That'll do suffice to say that there are many varied factors. In Europe kids live with parents waiting for them to die so sadly thats where NZ is heading. Unless Govt.frees up land ,funding infrastructure and introducing less complicated consenting procedures.It can be done but of course ,as you say, a reducing price market isn't going to be a vote winner . See my post above. A gigantic 'reset' is just around the corner for NZ

Interest has always gone up and down. It is like the Tide. You have to prepare in advance for it.

By the way, some of Europe has a system where very few own a Home. the land is just too expensive. But Rents are more affordable. Some place have bare apartments. And I mean bare. Nothing but white walls. When you move in, you do everything. Fit modular Kitchens, do your own colour scheme and so on. When you move out, you have to strip it back to bare again. But people tend to live very long term in these places. In Austria, the Renter is responsible for the safety of everyone in and around their building. Enev to the point of clearing snow away of the foot path each day to ensure peoples safety as hey walk past.

There is one factor no one has touched on yet. Culture. The way we White European Wealthy (so they tell me) Folk view life vs the way Maori view life is vastly different. I am not saying either is right or wrong. It's just different.
It is very much the case of the Mexican Fisherman vs the American Businesman story. The Mexican sitting under the Palm Tree playing his Guitar and enjoying life. While the Businessan believes the Mexican should be working hard, building a business so he can retire and have exactly the same outcome. Neither the Mexican or the Businessman is right or wrong with their views of life. But both think the other is being silly and missing the opportunities life can give.
Now think about the fact that we White European Folk often expect Maori to have the same view of life as we do. Most expect Maori to get a good education, earn a good wage and be "hard working valued contributors to Society" (as I have heard it put). Many Maori don't see it that way. We don't understand and shake our heads in disbelief that they don't get it.