which is why infrastructure projects should all be privately funded, then their economic viability, success or failure are on the backs of the owners and not tax payers.
Let's explore that thought a bit.
Say the local islanders dislike Mr. Ellison's policies. Say, for example, that someone wants to start a local airline which competes with the ones that already serve the island. Well, the ones that serve the island are owned by Ellison, and any competition is going to eat into profits. Fortunately (for him) he also owns the airport, so he can just refuse to allow the 3rd party airline to fly there.
Of course this competing airline could start their own airport, but that's likely prohibitively expensive. And even if they had they money, Larry owns all the land on the island, so he can just refuse to lease them land on which to run an airport.
The inhabitants of this island are, for all intents and purposes, indentured peasants to Larry Ellison. He has an effective monopoly on their food, housing, and transport off the island, and they have only as much say in how he runs things as he feels like letting them have. If you honestly think that's a good way to live, then I'll be happy to purchase your house and vehicle from you and let you pay me rent (at a rate that I choose, of course).
Of course Lanai is an extreme example, but similar problems occur when you try to run certain types of infrastructure projects with private companies on the mainland. For certain classes of things like roads, water/sewer lines, and probably electric, the amount of space and planning required makes it prohibitive to build multiple competing services. You can't have a city based on TWO separate street grids. And trying to run more than one water system or electric grid through the same town would get intrusive and immensely confusing in all but the most sparsely populated areas.
So what you end up with out of necessity is either a government monopoly or a private one. You no longer have the ability to "take your money elsewhere" so the private company has zero incentive to listen to you. With the government monopoly, though, you get two major benefits: one, you're guaranteed a vote, and in a local government that means a lot more than at the federal level; and two, the government's goal is to serve the needs of the citizens, NOT to make a profit off them.
In short, you've grossly oversimplified the problem. Of course private corporations COULD own and run infrastructure projects. Nobody's disputing that. But it's highly unlikely that they would run it WELL in cases where competition isn't feasible.