See the Route 91 Express Lanes which were built even though there was heavy government competition from route 91. Private companies can and do take up huge projects all the time.
91 Express Lanes - Wikipedia, the free encyclopedia
After all, it was private companies that built the subway system in New York, not the government.
That is a 10 mile road, and isn't it owned by the government? That linked said it was owned by Orange County Transportation Authority. Regardless, 10 miles is not a "huge project" on the scale of highway development and maintenance. There's 1000 miles of interstate between Colorado and Illinois, that's just I-80 and just in that section, it goes on further. That one section of that one interstate is already 100 times greater in scale than that of the Route 91 Express Lanes.
The bulk of actual scientific research is performed in government labs because government provides a ton of money such that the profit of private investment is severely compromised. Private companies tend to piggy-back off of the research done in government labs. However, it's interesting to note that most of the supplies used in those labs comes from private companies.
It's preformed in government labs and academia because government is the only entity with the time scales and pocketbook necessary to perform the aggregated volume of scientific research necessary to maintain and proliferate the growing technical needs of our society. Private companies can and do invest, they're ability to do so is in no way, shape, or form compromised. If Agilent wanted to give me 500,000 bucks for research, they can. But they don't, because they have little interest in quantum computing. The government, on the other hand, has HUGE interest in it. Society cannot advance through stagnation, and technologically developed and advanced cultures like our own need continual input of new technologies to continue moving forward. The private sector does piggy back incredibly hard off of that research. And that's the point. The research is not necessarily profitable to government itself. But government is the only entity capable of supporting the entire aggregated system. Private sector then reaps huge benefits from it, even though the the government investment may not reap profit.
We buy all our stuff from private industry. There's no government company for laser frequency doublers or acusto-optical modulators. I buy those from private companies. But guess where they got that technology from? That's right, it's all formed from base scientific research. Some poor grad student spends his career and post-doc messing with something, say ring lasers or dye lasers or doublers, whatever. After he/she is done, they can (and many do) go off and start a start-up to start making commercially available products for academia. But their input to research is perfecting the already established technology and engineering a practical, commercial use. It's not the broad band experimentation necessary to find and understand this phenomenon in the first place. And it's expensive. I just bought 4 lenses, 1" by 1", little cylindrical lenses for UV (221 nm) lasers. Each lens was over 500 bucks a piece. I should be in the AR coating business for sure!
But this is part of the point. People say that government should run like a business, but it's not true. Government should run like a government. There are things that government can do well and things that it can't. The same with private enterprise. Those things are different. So government can provide something, it doesn't even need to be profitable because government can survive long time periods without being profitable (unlike business). But because it can do this, it can invest in things business cannot. Business can then pick it up on the other end and find ways to make, in this case, commercial products for sale. The two entities then feed off of each other. If you set the fail conditions of government to be the same as the fail conditions of business, then you will find yourself in a situation when government itself fails from not being profitable. Then we're really up ****'s creek without a paddle. Government needs to operate like government, business needs to operate like business. And the synergy between the two creates a wealth of benefits for us on whole.