They wouldn’t come if they knew they would be stopped. We can (and do) send aid when needed, even though our countries are under no obligation to do so.
Sometimes the aid needed is a place. I have no idea what you mean by obligation or what axioms you base that conclusion on but it seems somewhere in all of that we disagree. I think we should provide people a place if they need it when we can afford to. I think, for one, it's cruel not to do so, but secondly it's good to promote a norm of doing so. We may be in need of a place some day (think war, climate change, economic crisis, etc.) We can't do more than we can do but I think we should do what we can to help.
