An uninhibited free market would absolutely produce a price for that service. If no mail is sent, it's because the market is inhibited or both of the parties (government and families) are unwilling to pay the price.

What will happen is that they'll continue to vote overwhelmingly Republican, as a bloc.

Edit: This isn't political snark, FWIW. The deleted parent comment pointed out that soldiers on deployment rely on the APO/FPO system under USPS to receive packages from home, and wondered what the soldiers would do if the USPS is allowed to fail by the Trump administration.

It's objectively demonstrable that those who end up worse off because of Republican policies are among the most faithful Republican voters, and that almost certainly holds true in the armed forces as well. Warfighters and their families will likely pay more, get less, and continue voting the same way.

Soldiers don't have access to the internet?