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.