No, that graft is an unfortunate property of all profit motives. It is no less prevalent, nor any less harmful, in the private sector. 
You are just suffering from some rather severe confirmation bias where you cry over the pains caused by government failures but overlook those caused by private sector evils.

I do not make that mistake. I consider them both to be terrible. And equally terrible - just at different things. 
So let government do what goverment is least terrible at. And let the private sector do what they are least terrible at.

And as a general rule - if it's something where even people who will never use it benefit from it's existence (like public transport) government will likely be the least terrible at it. And when it's something that is a fundamental human right to have -the very IDEA of letting somebody profit of it is utterly unconscionable and tantamount to mass murder,