You say government to go into "profit based business", but what is a profit based business? What isn't? Any social interaction can be the basis for commercial exploitation. Profit can be made from education, health care, local level police (private security), national security (private militias), utilities, etc. Who is to decide what should be a "profit based business"? If a private organization offered protection (read, retribution) from criminals, and made good profit out of that (and assume said organization obeyed the law), should government shut down the police to avoid competing?
The problem with free markets is that even when they work, they find a solution that is optimal in some ways, but that may be quite far from the best solution for society as a whole.
A privatized water company in south america will set its prices to optimize its profits. If the resulting prices mean 5% of the population cannot afford clean drinking water, so be it. The cost is not high because it must be, but because that is the free market solution. The social costs of high water prices are external.
Similarly, a private communication company in the US will set prices to optimize profits. Society may benefit from wide spread connectivity, but the company does not, so that will not affect prices.
In summary, competition of government with private sector is not the main issue. The issue is which services should be private and which public. In the interface, there may well be some areas where private and public coexist (education?) Publicly run services can be as corrupt as private corporations, and are generally less efficient, (but do not add a profit margin to the overall cost).
Of course, such decisions have far reaching long term effects that are frequently ignored. see e.g. the US jail industries massive lobbying for longer jail sentences, and the resulting incarceration rates.