Radio, telephone and trains were all private inventions, developed for money. The Internet was explicitly not commercial for many years.
So? The outcome of wars are almost entirely decided on the basis of logistic and communications systems. It's hardly a relevant matter to point out that research into communications and logistics has military value and would originate from military funding.
This is not something one needs to 'keep in mind' to conclude that commercial entities would end up controlling and administering it.
FWIW, Samuel Morse obtained a $30,000 grant from Congress in 1843 to build an experimental telegraph line between Baltimore and Washington.