You can see this playing out in China right now.
Since one can't predict with any confidence how long one will live beyond 'probably 50-110 years if I don't get hit by a car', retirement savings is much easier when there is a government-provided income floor in case of mistakes in retirement planning. Otherwise, how do you choose between saving enough that you're 80% or 90% or 95% or 99% or 99.9% sure that you'll have enough income for the rest of your life? And if you wish to buy such insurance (an annuity) in the private market, how do you spread risk so that you don't face risk that the company will fail? And how do you make sure that any financial adviser you have doesn't exploit you as you decline mentally?
Or do you just save single penny possible and never consume anything? Buy an apartment building and hope like hell your neighborhood doesn't decline? Buy a portfolio of widespread rental houses and try to manage them when you're 85 and have cancer? Hope your children are loyal? Or spread risk by having 6 or more children?
Historical experience suggests the outcome of attempts to leave such complexities to individuals is widespread poverty amongst the elderly.
And that's not even getting into the question of whether we have a global savings glut. Safe investments are getting awfully expensive, with negative interest rates on some government and corporate bonds being sighted lately.
Insurance companies who sell annuities are have credit ratings, and some have been around for quite a while. Metlife was founded in 1868, Prudential 1875, or of course Lloyd's of London 1688.
Mental health decline is of course a concern. If you trust your children, or a younger relative, it's a good idea to give them durable financial power of attorney ahead of time.
There's no disputing that a social security scheme, or a paternalistic compulsory saving scheme can decrease poverty in the elderly, especially if people are hyperbolic discounters, but it also has downsides.
1) There's a risk that a compulsory saving scheme can be nationalized by the government, as it happened in Argentina for instance.
2) In social security schemes, the money is typically invested but rather spent directly by the government. The hope being that the future tax base can pay for the liabilities. The model has proven unsustainable and eventually requires that government resort to inflation, fiddle with the retirement age, or cut benefits.
3) The money paid into and out of social security is controlled by the government, which gives it a lot of political power. Governments often use their money for nefarious purposes such as wars, cronyism, corruption, etc. Giving them more control can be a bad thing.
4) There are moral concerns with forcing people to participate in a financial scheme against their will.
Money has to be lent to be saved, of course, someone has to spend it somewhere. If your country has an overly high savings rate because of a poor social security system, it's going to hurt one way or the other.
I think having a high savings rate, all else equal, is actually a boon. Low time preference means that more ambitious, longer term projects can be realized. This raises the wealth of the population overall, further increasing the fraction of money that can be saved, and creating a virtuous circle of civilization.
By not eating all the food they had and saving it, the first humans were able to not go hunting/gathering for a while, and dedicate that free time to building better tools. Those tools further increased the productivity of hunting/gathering, and enabled them to save an even greater portion of their food, freeing even more time to build even better tools, etc.
This could be said about the US too.
