That is emphatically not what his comment stated, nor how the effects work.
The specific argument is that by spending $1 to provide a service to a group of people, you increase the size of the economy, and consequently the tax base in that area, by more than $1, thus turning a net profit.
Game theory. The population centers voted that failure to respond to mail can subject you to severe legal penalties, including imprisonment, and there is at present no practical substitute to first class mail. Cutting off the mail would result in unfair punishment of remote peoples, which would result in secession of the remote territory, which would result in loss of EXTREMELY valuable roads, railways, pipelines, oil tank farms, air space, geographically-defended military bases, and radio spectrum.
To put it another way, the economy of scale of the Pax Americana can afford quite a bit of abuse from the postal unions.
If settlement of remote areas is a good investment then it will occur even if the settlers have to pay the market prices for their services. Arguing for subsidization is an admission that settlement is not a good investment.