Many do. The cost to society is enormous.
If housing and labor markets were entirely elastic, and those are the only two factors your people need to consider, then "go away" could be a reasonable government policy. But people are more than their income and their cost of living.
Consider a recovering opioid addict making minimum wage. Medicaid for health care. They are recovering, not relapsed, because of great support from their parents, brother, and grandparents, all of whom live in (say) Oakland. If we look at the labor market and the housing market, the rational economic decision is to move away. Away from their family, the support network that keeps this person employable (and quite possibly alive). Should the whole family move? Not all jobs are everywhere. Should the brother quit Berkeley? These webs are not easily untangled.
If their support network were a Church, or a local football club, the cost would be same: leave your life behind so the Bay Area can stay suburban.
Expensive housing destroys the small, vital institutions that hold our society together by driving people apart.