Yes, the Private Sector is "there" to appease either the shareholders or the business owners by creating profit. It's that pursuit of profit that keeps overhead low. Now contrast that with the Public Sector. They are only "there" to appease themselves. Making a profit isn't part of the equation. Government employees don't lose their jobs if a profit isn't made because their jobs can be maintained by increasing the national debt. Overhead can increase every year because there is no concern over profits. I challenge you to show me a governmental agency that's gotten smaller over time!
As for your claim that when profits start operating at a loss they close up? Well, yeah...but that usually occurs when either another Private Sector company out performs them...or increasingly when the Public Sector encroaches on their market.
As for different types of learners? Granted some students don't do well in some learning situations. For them a more traditional format might be the only option. For those that CAN function well with an internet form of teaching...they would be receiving the best teaching available at a far lower cost because that one professor's recorded lecture playing over the web could be seen by literally millions of students rather than a few hundred. THAT is a viable way to reduce the cost of education...making it a function of government won't reduce the cost...it will simply change who gets stuck paying for that cost.
It's not necessary to advertise the public sector. The public sector is there to provide a service. Hence, the public. Time and again we see the private sector fail to provide the same service because profit comes before people. They have failed at
everything they have undertaken simply because they cannot provide the same service and make a profit. This is true in mental health care, physical health care, nursing homes, social services and education. The goals are different. This is why they shut down. It has nothing to do with the government encroaching on a market. The government service was stopped because the cry was that it could be done more efficiently and with less cost to begin with. Furthermore, many of these hacks are dependent on government money (tax dollars). So, when they figure out that they can't make a huge fortune doing the hard work then they bail. That is what happens. Every time.
We are no longer in the widget making business. The widget jobs were outsourced. Research is not done behind a lap top. Fieldwork is not done behind a laptop.