Privatizing infrastructure is extremely positive if there's any chance for competition to arise - for instance, Italy has moved from a monopolistic state phone company to a well regulated and open free market, which has caused a boom of competing companies that has massively driven prices down. I now pay €27/mo for unlimited 1Gbps/300Mbps fiber and €7/mo for my phone plan with 50 GB of data, unlimited calls and unlimited SMS.
This is offset by the sad state of our highway system, which has been handed off to private companies a long time ago. There is obviously no way to create competition in highways (what are you going to do, build a cheaper highway next to the already existing one?), so the main company (API) has been neglecting mantaining infrastructures up to the point that a few bridges have collapsed, killing people and creating huge preventable disasters. Tolls are also crazy expensive, often amounting to half the cost of a road trip (and here petrol costs €1.50 per litre).
There's no incentive for a private company to invest a single cent as soon as it becomes a monopoly, it is something that has been known since the dawn of man.