Ok, let's assume we do this, scatter the poor across the land.

How do those people, who typically are in greater need of healthcare, education, daily living assistance, transport assistance etc. due to not being able to afford preventative care going to access the services they need the most? I already hear about people in the US travelling many hours one way to see an insurance-authorised specialist for a chronic condition.

Doctors and social workers and teachers aren't exactly lining up to work in the Appalachian mountains. We are also more frequently hearing about industrial rural towns having their water contaminated through companies spilling and dumping waste. Scattering people across the land without sufficient infrastructure is an 'out of sight, out of mind' solution. Cities are the only places which have the resources to support people at larger scales for a variety of different issues, when people are also expected to work 40+ hours a week during standard business hours.