https://data.bls.gov/timeseries/LNS11300000More infrastructure won't change the percentage of kids, disabled, elderly people, and college students without jobs. It won't change the fact that in a dynamic, growing economy, there will always be some transitional unemployment (note that we deliberately target an unemployment rate of about 5% to keep inflation in check). So, yes, it absolutely is an argument for some form of safety net.
Poverty in the developed world is mostly a life cycle issue. Also, even with full employment (which we're pretty close to now), a quarter to a third of the population will be in poverty absent transfer payments because of the way market income distribution works. That's why every country with a market-based income-distribution system has independently developed a safety net.
Doesn't look like full employment to me. Are you saying that the able-bodied people who choose not to work and you choose to be poor do not affect the numbers?