From an European POV, you Americans already push stocks and individual retirement savings like they are a golden calf with your 401k plans and the slaughter of actual pension systems.
As for home ownership: it certainly is better in retirement if you own your paid-off home and only have to foot property tax, utilities and a savings fund for renovation out of your retirement accounts or pension payments.
What are you talking about? Government-run pension systems, or company-run ones? The government-run one is called "Social Security" and it hasn't gone anywhere, and certainly hasn't been "slaughtered". It hasn't changed in ages really; the problem is there's fewer contributors and more recipients now due to population aging, so when the surplus runs out in 15 years, it'll be restricted to only incoming funds, so recipients will receive less.
Company-run pensions are indeed dead in America, for good reason, being replaced by 401k plans. Why would you want your retirement security tied to your former employer? What happens when the company mismanages the pension, or the company fails? This has happened many times here, with older people losing everything except the social security which isn't that much. That's why they moved to the 401k system, so retirement funds are put into the hands of a better-regulated 3rd party financial firm to be invested in securities.
I don't see the problem here. I have my issues with many things in America, but this is one thing they did right. It could be better: some 401k providers are much better than others, for instance (some have poor securities selections available, some have high fees, etc.), but overall it's much better than the old days of having a company pension.
What happens when the economy tanks? The fact that so many Americans have tied their post-work existence to "stonks only go up" is a damn perverse incentive for the US government - as it now has to think "what will the stock markets do if we introduce political measure XYZ" every time. Strong environment regulations for oil and power companies? Regulation for social networks? Is this a good idea when a lot of your people have a sizable exposure to these in their retirement accounts?
Meanwhile, here in Europe, pensions tend to be financed by the pension contributions of the current working generation. It's not perfect, far from it, but at least our pensioners don't have to fear random shit wiping out a third of their pension funds (assuming a 100% investment into S&P 500 [1]). We don't tie neither our pensions nor our healthcare to our employer (or even to being employed).
[1] https://www.statista.com/statistics/1175227/s-and-p-500-majo...