If you remove all welfare for the elderly then it does provide a strong motivation for people to have and raise children who might take care of them in their old age....and to save for their own retirement.

New Zealand was the first country to introduce a (very modest pension) in the 1890s, apparently for guys who had come here to mine gold, never married and were now unable to work and had no family to care for them.

I do not think we can politically return to zero welfare, but means testing welfare does go some way to restoring market incentives and the potential for families to take more care of themselves rather than dependency on the state.