Life can be very harsh if you're unfortunate but don't qualify for government benefits. Or maybe you've genuinely turned a corner in your life but government rules don't have mercy like individuals can.
But yes, unfortunate you if you get something that's not covered under the universal deal, e.g. some kind of leading edge cancer treatment. That's when you hope your private insurance (if any) will pick up the tab.
The government doesn't literally pay for anything you want or need. It picks what things it will pay for and what things it won't. You can't always ask government to make a special exception in extenuating circumstances like you could with a parent or cousin.
I'm not saying family is always better. I'm saying there are certainly downsides to government-based charity.
That's a perfectly respectable opinion. And you and I probably are in agreement on the government's role on many of these kinds of social issues. However, it's completely possible to both support those programs and simultaneously understand their impact on social fabric.
Do you really suggest "having a big family" as the way to survive health problems and retirement? Because that's how it works in some (e.g.) SE Asian countries, and life there can be very harsh indeed if you strike adversity and don't have family to care for you. Some people are infertile, or have lost their children.
Not to mention that simply populating the world with more and more people is kind of environmentally short-sighted. I'd rather have the government bulk buying my meds, and lighten my overall footprint on the planet, rather than harking back to ancient times when there was little or no government, and family was everything.