Nah, there's much more than roads in a welfare state.

There's a nationwide pension fund, unemployment "insurance", long-term care insurance and what not. All of this is cross-financed in a mix by everybody who's paying into it.

Also: Lots of people switch from private health insurance back to public health insurance once they get old, because then costs are rising. A welfare state also supports those who have "suddenly" become poor so they had to make that switch... ;-)