how will that quickly fix inflation ?
Also, investors won't start exiting the market if they expect expansion in housing stock. Financial markets trend, they absorb information imperfectly, they overreact, and there is massive volatility as all this occurs. Indeed, there are some investors who base their investment strategy on the inability of markets to react to capital cycles (Marathon Asset Management have written books about this). Investors have different time scales, if the housing stock was going to expand then you would see capital pile into the sectors because people will chase that growth expecting to flip at a higher price at the top.
When you own a home, whether you've paid it off or have a mortgage, you can sell that home and convert it back into currency that you can use for other things. Even better if you can improve upon the home in ways that increase the resale value. Depending on the state of the housing market, it gives the potential to hedge inflation. Homes can be inherited and passed on to descendants. Perhaps one could hold their wealth in precious metals as an alternative, but those metals don't provide value until they are cashed out. A home, on the other hand, provides constant value because you get to live in it and do with it as you please (HOAs and other regulatory bodies notwithstanding).
When you rent a home, you are paying to pretend like you own the place. You cannot sell the home, any improvements you make to it benefits the landlord, and you cannot put your home in a will. In other words, when you hand in your rent check every month, that wealth might as well have disappeared into the ether.
It's hard to speak for other parts of the world, but my experience in California is that the concept of a "starter home" is a thing of the past. Yes, there are swaths of small homes that may become available, but one that isn't horribly dated can be hard or in disrepair to come by, and these days the price of an existing starter home is pretty outrageous. Whenever you see new construction, typically it's one of 4 things: mansions, McMansions, condos, and large-scale apartment complexes. My assumption is the reason you don't see new starter homes being built is because the only way for developers to make a meaningful profit after years of fighting for municipal approvals is to build one of those 4 types of homes I mentioned because they have the highest return upon sale.
Seriously, just take a tour of the Southern California area. You are unlikely to find new single family homes being built that aren't McMansions. Nearly all of the starter homes that would be appropriate for a young couple and a couple of small kids are occupied by retirees, are in need of renovation, and are in less favorable areas.
Maybe it's different around the rest of the country and the world, but with the way the housing market and the economy are going, as well as the direction that UN governments want to take things, I predict that will be a spreading and continuing trend.
If it wasn't so costly, time consuming, and an overall hassle to build homes of various sizes, more people might be able to maintain and build wealth even in the face of inflation. Otherwise, their currency mostly sits and rots, or gets lost in bad stock market gambles.
Hell, just try building a "tiny house" and see how that goes. Many of the people that build those have to build them on wheels for a reason, and not necessarily because they want a quirky portable home.
EDIT: Oh, and about the labor force thing... if people have the hope of being to able to own a home and build their own little fiefdom like their parents and grandparents did, they might choose to participate as opposed to being part of the mass workforce exodus we've seen recently. After all, if you have no hope of owning a home and you probably won't retire, why spend your life working hard rather than just working minimally to get by? Even I would work way harder if I didn't think that home ownership would be futile or at most a Pyrrhic victory.