There's a couple interesting issues at play. One is that a profit incentive can be at work without the goal being to break even. For example, perhaps the goal is to subsidize by only $XXX million/year and above/beyond this goal is considered "profitable" with appropriate incentives.
Another is the issue of correlation/causation. Well-run systems may tend to be efficient in their use of monetary resources (almost by definition), but it's not clear that setting a for-profit goal will be a cure-all intervention that causes a system to be well-run.
It's also a big leap from setting profit goals to full-on privatization, which I'm skeptical of for several reasons. Private companies are often only pushed to be "good enough", better than the competition. A public transit system that is just barely better than a cab (say for daily work commute) is no good at all. Private companies tend to have short-term incentives, for instance, the CEO may get a bonus based on the current year's profit, which will be destroyed by investment in infrastructure. Companies care about maximizing revenue rather than welfare. Etc.