Social welfare state will still exist, it'll just be more costly as drag than it is today (in the US, ~$1.1T/year of uncompensated caregiving occurs, for example). Capitalism is more the challenge, it's built on squeezing the aggregate working age population for profits, and that cohort is in terminal decline over the long term. Between global sovereign debt load [1] and the demand for future profits (slides 31-33 of this PDF), there will be sadness as the future has less and less humans to saddle these economic burdens on. Such are the breaks when you predicate a socioeconomic system on never ending growth, and growth is over because humans globally (for various complex and interwoven issues) are choosing to have less children or no children.
[1] https://unctad.org/publication/world-of-debt ("Global public debt surpasses $100 trillion in 2024.")
A tfr of 1.7, the welfare state will be costly but exist. A tfr of .73 like korea has? Long term, that’s 1 20 year old and 3 45 year olds taking care of half a baby, 7 70 year olds and 10 95 year olds
70 year olds can work, and will have to. Already in many places you have two positively ancient people where one is the caregiver for the other.
People make it work because they have to, but the pressure of taking care of even more will further reduce the desire to get ahead - that has another mouth to feed.
It is what it is. You do the best you can with what you have.