ARPANET was the founding technology of the internet. The fact that DARPA was a larger umbrella tells us nothing about the amount of capitalist investment (which was $0), so i don't know why you bring it up, as if it was relevant to your case. All the knowledge and technologies, coming from various agencies and universities, was inter-disciplinary and was government funded, sometimes for decades. I repeat: a free market capitalist society would have never created the internet, as no capitalist would have invested without returns for that long.
As for the efficiency of capitalism, it has massive externalities that make it inefficient and even more ecocidal than other forms of industrialism. The species being brought to extinction have more value than humanity itself, so of course that an economic system that destroys more value than it produces cannot be efficient. And the idea of capitalism without government is only abstract. Government is, and has always been mainly a tool for capitalists to socialize risk and privatize profit, and protect or expand their stolen property through violence (police, military imperialism). The public can have some democratic say (more than they do in corporations, which are purely capitalist-run), but as my documentary shows, parties in elections are generally groups of capitalist investors who compete to control the state. Wage labor itself, generally entails money confiscated by virtue of a "work for a boss or else" social environment collectively imposed by capitalists, which allows them to exploit others and brainwash the masses into thinking that their activities are worth huge amounts of money. And thus their "risks"are always with other people's money. And of course, the risk of workers who risk life and limb is much greater, and yet they get paid less. Slave owners also took risks btw (their expensive slave could have gotten sick, died etc). That doesn't mean that the slave owner deserved profit. Some slaves could even buy their own freedom and become slave owners themselves. That social mobility didn't justify slavery. With more democratic governments, in which the public has some say to compete with capitalist control, some of that money confiscated by capitalists can be redistributed, achieving a fairer society. Of course, capitalists love to form unions (chambers of commerce) but hate when workers form unions, and use the power of the state to prevent it. A more fair arrangement, would be for people to earn money according to effort and sacrifice toward a socially useful task, to be determined in a participatory manner by worker and consumer councils. Anarchist catalonia in the 1930s, was probably the best model that one could follow within an industrial system, and the least bureaucratic. So-called libertarian capitalism is far more bureaucratic, even in theory. The word "libertarian" was always used for libertarian communism aka anarchism, anarcho-syndicalism or council communism. Some jokers in the US later stole the term "libertarian"and started using it in relation to capitalism. Just ridiculous. Capitalism needs a government and thus will always need government bureaucracies. Although corporations themselves form bureaucracies at least as bad as those of government. State capitalist societies like the US are far more efficient than more free market societies. And every country has tended to need a period of protectionism and government investment to build up their industry before they could compete in a more open market.
But in any case, as i already said, all industrial systems, from soviet style communism, to western style capitalism, to even anarcho-syndicalism are illegitimate for a simple reason: they cause ecocide to different degrees. Only a massive reduction of population/production (which seems to be consistent only with preindustrial society) reduces ecocide enough to be worthy of contemplation.