Is that because those who aren't capable of taking care of themselves just... die?

Economists have studied this extensively. Less substantial government social safety nets lead to higher personal savings rates. Personal savings rates reach as high as 40% in countries without social democracy.

This capital is managed by the individuals who will derive the entire benefit from it, so they are incentivized to manage it effectively, and not hand it over to inefficient union-run bureaucracies, which give their employees early retirement at 55 with massive pensions:

https://www.hoover.org/research/california-state-government-...

They are also incentivized not to be lazy and draw upon it, as doing so hurts their own interests, by depleting their own savings.

When people pay for their own expenses, their incentives are aligned with the goal of national economic efficiency.

Government, meanwhile, ultimately becomes a rent extraction mechanism, no matter what its ostensible purpose is:

https://twitter.com/SpencerKSchiff/status/125276128577685913...

In aggregate, I'm sure that's true, but there are all sorts in society, including people who have little capacity to earn money in the first place, let alone save it. That includes, for example, orphans, people with severe physical or mental disabilities, drug addicts, elderly people who lose their savings to fraud, and so on. Taking care of these people does create an economic burden on society that might come at the cost of some economic growth. But that's a choice, and for many people, a public social safety net that takes care of people in need is deemed worth the cost.

When you're falling out of a plane, it doesn't matter how strong your incentive to fly is. You aren't going to grow wings by incentive alone.

Sure, but that's not the primary reason it's better for economic growth. A far larger proportion of social program beneficiaries would survive in an alternate timeline where these programs never existed. As for charity cases, there are vast private social support networks that emerge in a society with lower taxes and less government-funded social safety nets.

It's not a perfect system with no one falling through the cracks, but it is a system more resilient to systemic collapse as seen in the USSR when it went bankrupt, and one that produces greater economic/social development overall.

The zero-risk bias means people prefer to bring one type of risk to zero, even if it means increasing overall risk. I believe that is what's at work with government-provisioned social safety nets. Economic growth reduces a host of risks. But a social safety brings one type of risk - that is actually quite insignificant relative to the rest - to zero. So people are willing to trade economic growth for unconditional social safety nets.