The other thing is, far enough out in the country, their numbers thin out because of geography. The further you are from the center, the less dense your numbers are. Plus they have to get past a large number of armed civilians, farmers, and other independent survival types. They will lose numbers through attrition so by the time they are a couple hours outside a city (by car) there numbers will not be in their favor.
The rural areas are what concern me. For a realistic assessment of how that would go, study historical accounts of the Indian vs settler conflicts, more specifically those of the Comanche vs Texicans. Country homesteads would fall like dominoes even to a less than sophisticated force. There wouldn't be any struggle about exposure or finding food by hostiles since working farms & ranches would have livestock and grain stores if not personal food caches from the original owners to subsist upon. If multiple such properties were captured by the same grouping of hostiles, that would present a sticky problem in the area - they would occupy and fortify as mutually supporting forward bases - until someone finally comes along to dig them out, if ever. Normalcy Bias would be a great asset to hostiles, at least at first until people got better organized like they did against the Comanche so long ago.
The Comanche were better versed in survival in the wild than most basement dwelling millennials.
That’s going to be their downfall.
I don’t doubt that in some areas what you propose is likely to happen.
A lot depends, I think, on where you are, how rural you are, how your state is on guns, how far you are from a big city and how big that city is and what they have to survive to get as far as you.
LOTS of variables in how people are going to fare if/when the cities collapse.