Giving the government more money to do things works really well. Here in the USA we've given the governments 3x more money in real terms to run our public schools, and we've gotten worse results over those 3 decades.
Governments also get to hide real expenses that audited private enterprises never could. The "cost" on this website assumes what's paid is adequate to manage the business which is wrong.
You present this as something inherently true, but really there is no reason for this to be the case. We could make it so government entities are significantly more transparent than would be reasonable for a private entity. In practice, that is already the case and what you said really isn't true, though I'm always in favor of more transparency.
It's interesting how once people were successfully swindled into privatizing everything, the rhetoric changed from "everything will be cheaper!" to "well of course it's more expensive, you want to reward them for their superior service, right?". Apparently none of these extra costs go to appeasing middlemen or lining investor pockets, all these companies clinging onto natural monopolies are just too good at what they do. They have no conflicts of interest whatsoever!