Why does social welfare need to be handled at the federal level? There seems to be no explanation for why people insist on this other than that it must be so.

Even as of today, California gives aid to many states who fundamentally disagree with California's culture. Make social welfare state level and some states will simply starve.

It's like insurance: we all need to pool together and help everyone. And for it to work, we can't complain that some people get more help than others. It's a safety net, not floor. If everyone hit the net, the entire thing collapses quickly.

2nd reason is that people can move between the states easily. Imagine the logistical disaster of having a California worker work for a New York company. Which social security does this workers wages get deposited to? What if the worker moves to Arizona? What if the New York company opens a branch in Florida and that worker's department operates out of there?

It's a mess across state lines, and traditionally we have state disputes handled at the federal level.

You are entirely incorrect, article IV prevents this.

And that misses the point entirely: parent's point is that greater mobility between states is a good thing.

Social welfare needs to be handled at the same level that mobility exists, because otherwise all destitute people will bumrush the nearest jurisdiction that is giving out generous welfare benefits. The issue is most often seen at the city level (e.g. Bellevue “encouraging” homeless to go to Seattle), but more generous policies like housing-first will need to be federally administered to prevent the most generous states from getting bumrushed.

Because Mississippi, Missouri, etc.

People should not be condemned to poverty just because they were born in the wrong zip code.