America doesn’t have a welfare state.
Economists generally love the idea of open borders. By some estimates a world of open borders would be $78 trillion richer, basically doubling GDP (Economist which has a subscription, or Vox). The free market works best if there’s free movement of labor, that’s just pure economics.
It’s only our emotions and biases that stop it. And the world did have open borders for most of history. It’s not going to suddenly explode.