Not a terrible idea really: Victorian times were also when the industrial revolution was happening, and unregulated coal plants and factories were belching out unimaginable amounts of pollution into city air. Getting away from that mess and breathing clean air probably was good for you if you had health problems.
The joke is they send people someplace else, and when it doesn't work they send them back. Guessing most city dwellers could not afford a doctor or resting up on the countryside or beach.