If anything I think your "many other networks" example reinforces the point. The private sector left to its own devices came up with tons of incompatible small networks all vying to be the juggernaut.
The government, when faced with much larger problems than growing market share, instead invested considerable resources into solving a problem in a way that could handle the needs of a large national government, and then later invested more resources into making that internet a public good.
Even if the government hadn't developed its own internet protocols (and standardized on a notional private sector one), the government would likely still have been instrumental in expanding the use of some other standard. E.g. Eisenhower didn't invent the road, but his Administration sure did ensure a lot of them got built.
And they also built gateways so they could interface with each other. The pressure to connect them together was enormous.
For another example, Unicode isn't a government standard, and has replaced the various earlier competing protocols.
http://en.wikipedia.org/wiki/Unicode#History
The idea that the private sector won't standardize has plenty of counterexamples. Ethernet, for another.
Just like if the Wright Bros had not invented the airplane in 1903, someone else would have probably within 5 years. We'd still be flying today.
I suspect that the number of inventions that would not inevitably have happened once the preconditions were in place is very small.
After all, as I mentioned previously, having worked extensively with computers before the internet, the first thing someone with two computers tries to do is hook them together.
Hell, I even did my own hardware and software to transfer files from my LSI-11 to a PC over a wire. The government couldn't have stopped an internet workalike from forming if it tried.
This country was very specifically founded NOT as a democracy, for the very reason elucidated above. If the mob wants to vote your rights away, they should not be able to.
Self-defense and transfer payments from one individual to another (i.e., welfare) are different issues fundamentally. We authorize the government to solve the problem of coordination---in terms of defense, we don't want a bunch of private militaries roving around the countryside. At the heart of this is the issue of rights protection: if one man steals from another, his rights have been violated and government must act in response.
However, if the issue is whether a man has a claim on another man's property simple because he "needs" it, this is not sufficient justification for him to take it by force. Indeed, most people would call this "theft". Why is it different if the thug steals a dollar in dark alley from you or if a government coerces the same action at the point of a gun? Because a majority have voted for it?
Taxes are the bill you pay for living in a place where the government provides some services.
When I hear someone say "taxation is theft," I think, what a freeloader.
Even if we narrowly focus on a particular system of "private property right protection", which was certainly not the exclusive focus of the founding fathers -- who also advocated slavery and were extremely protectionist -- that nonetheless requires the enthusiastic embracement of the majority enforcing its will upon the minority at the point of a gun.
The U.S. government has supported taxation from day 1, including for the purposes of funding collective welfare, e.g. collective self-defense. Current citizens pay for the democratic decisions of past generations all the time. Even if you don't drive, you pay taxes to support road and bridge maintenance. This is not "indentured servitude". It is how a democratic society functions.
How much do we owe? Answer: it is determined through a democratic decision-making process that weighs costs and benefits to our society.
Case in point: This very forum would likely not exist without the aforementioned expansion of government. DARPA and government funding for high-tech research to the tune of billions of dollars has been instrumental in the birth and evolution of Silicon Valley, and continues today (e.g. Siri, self-driving cars).