I think if you call it insurance it assumes you are entitled to something, but you are not. A future government can decided to stop paying or reduce payments if they want to.

I prefer what we have here in Australia where you are required to pay money into an account that is actually yours, with a balance that you can watch grow, and that you can withdraw as you need when you retire.

Is it true that you can actually withdraw it all the day you retire to buy real estate and then the government will start giving out a pension for you? This is something I was told by some Australians.

Not exactly:

    The Age Pension is designed to support the basic living standards of older Australians. It is paid to people who meet age and residency requirements. It is targeted through the means test to those who need it most. Pension rates are indexed to ensure they keep pace with Australian price and wage increases.

https://www.dss.gov.au/seniors/benefits-payments/age-pension

If you only have the house you live in (that's more or less median) and no income (from additional rental properties | other investments) then you might qualify for a pension.

Typically people might draw on their superannuation fund to provide a weekly income for themselves although they are free to use it for their retirement plans as they see fit.