There is no technological problem. We are already wasting more food that would be necessary to feed people who are starving.
Even USSR, at the height of its inefficiency, was able to build housing for most of its inhabitants. It wasn't palaces but it did its job.
And when we need we can somehow find a way to crank out vaccine to vaccinate entire countries. And these are given out for free (of course, we pay for them in taxes, but still it can be done...)
> Then there is the problem of the political class not unwilling
I think you meant "willing".
Here, this is the problem.
When you say it is "political class", what you really say it is not your problem. And this is the cause of why this is not getting solved.
Because the problem is really you and other people like you who think it is not their problem.
If the people decided it is a problem worth solving and supported it with their votes, the "political class" would follow and solve the problem.
The "political class" responds to what is on peoples minds and to what people want. If people decide to spend their focus quabbling over building big walls or election results or vaccine efficacy, guess what is not getting solved? Anything else isn't getting solved.
Exceptions applied (mothers with young kids, registered artists), but otherwise this was enforced and if you stayed out of work for a certain period and didn't have a valid employer stamp in your papers, you would be chucked into prison for Parasitism (that was the name of the crime).
As a result, the Bloc had almost no visible homelessness, but this kind of solution would probably not fly in the West.
Just showing that there is no need for technological progress to build a lot of housing from public budget, only willingness to do it.
Roof over the head sure does the job. But in exchange a big portion of USSR population lived in essentially shared housing. You get a room and shared amenities (shared kitchen, shared shower, shared WC). In most career paths it would take a decade or more to be eligible for an apartment. And that apartment would be tiny. Got a kid? Great, you go up the queue and you get 1 room (kitchen + room, no living room) apartment! Got 2 kids? Nice, you get 2 rooms (not 2 bedrooms).
Of course, in some career paths it was much more comfy. A nuclear power plant built in bumfucknowhere? Well, anybody willing to go there even for an unqualified job gets a super spacious (compared to above) apartment on arrival. In exchange someone in a big city with no kids may be stuck in shared housing whole life with no chance to have his own apartment.
Perhaps the only difference is that low payed workers in Europe and North America have the option to live far away from their work and suffer long commute hours instead of the small living quarters. Although that option is starting to feel like it is forced upon us now as even the tiniest of apartments are also out of reach for normal working families in big cities.
The technological problem of feeding and housing every human on earth has been solved many times over. The logistics of distributing the available food and shelter to those that need is poorly designed and needs an overhaul. This is a political problem and can only be fixed with the political class that is seemingly unwilling.
Also public opinion rarely results in policy. Most Americans for example favor spending on green infrastructure to tackle the climate crisis, most Americans favor a more universal health care system, etc. yet the political class is hesitant.
There are some exceptions like China or various regimes.
But even Chinese Communist Party is very scared to allow their population to exchange knowledge freely, for fear they can just coordinate and decide together.
Think of it like a software team that has excellent developers but terrible devops. The developers have long long since fixed many of the bugs and implemented most of the features, but the devops is slow, corrupt, and incompetent so very few of the features actually make it to production.