Privatization is often a varied bag. Sometimes the contractor does a good job and sometimes a lousy job. Letting it be a directly gov't run process tends to get a consistent "C" grade, while privatization may get you an "A" sometimes and an "F" others. In other words, the variation is larger. This has also been true of schools and power utilities.
This tends to happen because the owners are usually a relatively small group of people or an individual, and their individual personalities and changing goals will shape the quality of job they do. They may decide on a whim, "I'll milk out my fortune now and dump the problem on the public."
Where privatisation does fix things, it's usually simply because the process of privatisation gives somebody the political capital to implement massive organizational change, and that somebody happened to be the right person for it.
Conversely, when privatised infrastructure is a mess, it can be beneficial to have it taken over by the state. Again, the mere fact of doing so will give somebody the political capital to implement massive changes, which can fix things if that somebody happens to be the right person (or group of persons) for the job.
As a corollary, it would be possible to fix many "broken" state-run offices by enabling the right person(s) to implement massive changes. That's probably even preferable to privatisation in many cases: you still have the same risk that you didn't choose the right person for the job, but you eliminate the risk of them just cashing out.
This tends to happen because the owners are usually a relatively small group of people or an individual, and their individual personalities and changing goals will shape the quality of job they do. They may decide on a whim, "I'll milk out my fortune now and dump the problem on the public."