Obviously both types of regions need each other to maintain the modern style of living as mentioned, but in some kind of societal collapse situation you'd probably rather be on some isolated farm that could theoretically sustain itself. And I feel like if those areas chose to go on with less subsidy money they could do so, but it's not a bad trade for food and everything else that comes from them. If one really wanted to hold the other hostage the one with the food would win.
That doesn't make them self-sustaining in modern society. And saying that roads are a luxury seems to be incredibly ignorant of how society evolved and how important trade routes (as well as ocean access, something cities generally have) for getting resources you otherwise don't have access to. Such as materials, spices and meds. Something that, you know, an isolated farm wouldn't readily have access to.
Especially since salt is kind of a big deal for food preservation.
Your "state level" explanation seems to ignore states that don't have major metropolitan areas.
The economics at the state level, play out just like how they do at the national level. The high population, economically vibrant parts generate tax revenue, which is redistributed to the sparsely populated, economically depressed areas, of which are not self sustaining, no matter how much the net receivers think they are.