Competition is the solution for corruption. Privatization often helps in fostering competition. But a private monopoly does not seem better than a public one.
In most industries, a private monopoly can't exist without State sponsorship. That'll mean it's corrupt from the very start. Exceptions perhaps being "natural" monopolies such as water mains.
Look at the cell phone industry in Canada, there are 3 companies all of which no one in the western world has heard of. There's the good (rogers) the not so good (telus) and the outright bad (bell).
Bell was state sponsored and still has all the protections of it. Last year they sent out 'free' wireless router-modems, however if you didn't subscribe to the service that gave you it for free then you'd get a bill essentially saying 'pay us $200 or send back the modem, or we'll take you to court'. The multiple late payment notices requiring payment 3 days before the bill could even be paid was the last straw, our phone and internet is being switched and bell can go stick their modem up their corrupt and incompetent asses.
Rogers seems to be the only competent cellular company in Canada. This is probably because it was independently owned from the beginning and the original founder apparently kept a lot of influence until late into the game (he died like this week). They didn't hike their SMS charges (bell and telus doubled it by charging for incoming messages), however I can't speak for the quality of their other services as I have a Rogers cellphone, which is because when I came here with a T-Mobile UK phone it switched to Rogers and they seemed competent enough... I was really vindicated in my decision when the competitors hiked their prices, however mocking my wife for it wasn't a wise choice.
I didn't dispute that State sponsorship may contribute to a private monopoly. I pointed out that corruption may add to the barriers to entry which would help a private monopoly persist, i.e. state sponsorship is not a necessary requirement for a private monopoly.
Your example also seems to demonstrate that state sponsorship isn't sufficient to grant a private monopoly.
I was thinking more the other direction. Corruption acts as a additional barrier to entry (will I get that contract? I can try and pay more money/bribe the right people, but even if I do that maybe there's a family connection I don't know about). This reduces competitive pressure, making monopoly more likely.
I'm not sure that increasing competitive pressure would decrease corruption. I can see how it might help, but it might also hurt.
e.g. a previously minimally corrupt business owner finding it harder to compete succumbs to temptation to join in the game due to increasing competition. So I think that part of it could go either way.