This was a very unfortunate trap that many western governments fell into in the latter part of 20th century. It's not really about wealth per se. but forced saving for retirement (i.e. reducing government responsibility for elder care).
That's a bit of a non-sequitur. The economy pays for elder care no matter what, and mostly our governments remain responsible if people haven't saved.
Plus we get emergent outcomes in our economies for systemic reasons - blaming our governments as though they are effective at controlling everything makes little sense.
Even if true it seems unlikely to be a primary reason, although it could be a partial reason.
That's the point of it being "forced saving".
Look, I'm not saying the government steered everything or even that they thought it through very far. I'm saying that they constructed a bunch of programs (in US, Fannie/Freddy, mortgage tax break, etc. similar other countries) to subsidize and incentivize house ownership in ways that economists hate (creates market distortions). Couple this with policies that support growth of houses as an asset class effectively has people saving pretty aggressively in a way that will typically be available to them in retirement. Less people with no assets upon retiring means less load on government programs. Implicit in this is left to their own devices, most people don't save as effectively.
The trap part is this: once this system has momentum any abrupt policy change will result in a lot more people being directly dependent, or more directly dependent on government programs in their old age. This will have massive budget impacts and governments know it.
The second part of the trap, which we are seeing now, is that if you make housing too effective as an investment vehicle, it will be financialized and further distorted away from effectively functioning as housing.
It's not just financialization of housing - as you note there are emergent outcomes in complex systems. For example, end of life care would probably look a lot different if it wasn't often effectively drawing down some of these savings.
It isn't really savings: it is a giant Ponzi scheme that depends upon the population cohorts aging and working and getting mortgages.
I'm in New Zealand and immigration is a primary driver for our house prices. Overseas owners will also drive house prices when we allow that again (our economy is strong but I suspect we will need to sell the family silver eventually).
If you are below 50 it is difficult to apply your implicit knowledge of the current steady-state to the future.
Italy and Japan have houses for sale at $0.
> saving [that] will typically be available to them in retirement
Currently.
I'm suggesting to try and take care to avoid inductive reasoning when looking locally at older cohorts and applying your knowledge of their experiences to your planning.
Of course as an individual you don't have a lot of choices to avoid the economics of your particular cohort. Understanding and mitigating your personal economic risks is trés difficult.
Using the word "savings" for your house is extremely self-deceptive in the longer term IMHO. Especially because the vast majority of what you spend is on interest not principal. I'm not saying paying for interest is avoidable or worthwhile, just that using the word savings misleads oneself.
Plus I deeply mistrust governments to do long term planning. The biggest drivers of our economic wealth seems to be unplanned emergent results of capitalism. Governments will turn to taxation and other means when an aging population turns out to be a problem. Our Green Party in New Zealand with about 10% of the MMP vote already suggested a policy of a wealth tax if you had saved over $1 million.